Chapter 6 of 14
Chapter 6: Be My Multiple, I'll be Your Factor
मैं तेरा गुणनफल, तू मेरा गुणनखंड (बिल्ली-चूहा खेल, म.स.प. एवं ल.स.प.) | CBSE Session 2026–27
Core Pedagogical Competencies & Concepts
- The Mouse and Cat chasing game on the number line: jumping intervals and escape holes.
- Common multiples of 2, 3, 5 and finding the Least Common Multiple (LCM).
- Arranging bangles into rectangular arrays and finding all factor pairs.
- Factor Trees for prime factorisation of numbers like 24, 60, 90.
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32...
- Multiples of 6: 6, 12, 18, 24, 30, 36...
- Multiples of 8: 8, 16, 24, 32, 40...
All Textbook Exercises & In-Text Tasks (24 Questions)
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Q1
Textbook Exercise • The Mouse and the Cat Game
The cat is on step 3 and can jump 3 steps at a time. The mouse is on step 15 and can jump 2 steps at a time. (a) What steps will the cat land on? (b) What steps will the mouse land on? (c) Will the cat catch the mouse before the mouse reaches the safety hole at step 28?
[4 Marks]
✅ Step-by-Step Solution & Working
Jump Sequences:
• (a) Cat steps (multiples of 3 starting from 3): 3, 6, 9, 12, 15, 18, 21, 24, 27.
• (b) Mouse steps (adding 2 starting from 15): 15, 17, 19, 21, 23, 25, 27, 29 (safe in hole).
• (c) At step 21: The cat reaches 21 after 6 jumps (3→6→9→12→15→18→21). The mouse reaches 21 after 3 jumps (15→17→19→21). Because the mouse was already at 21 earlier, and reaches hole (28) in 7 jumps before the cat can intercept it at the same moment, the mouse escapes safely!
• (a) Cat steps (multiples of 3 starting from 3): 3, 6, 9, 12, 15, 18, 21, 24, 27.
• (b) Mouse steps (adding 2 starting from 15): 15, 17, 19, 21, 23, 25, 27, 29 (safe in hole).
• (c) At step 21: The cat reaches 21 after 6 jumps (3→6→9→12→15→18→21). The mouse reaches 21 after 3 jumps (15→17→19→21). Because the mouse was already at 21 earlier, and reaches hole (28) in 7 jumps before the cat can intercept it at the same moment, the mouse escapes safely!
CBSE Step-by-Step Marking Scheme
Cat steps list
1 M
Mouse steps list
1 M
Step comparison
1 M
Conclusion: Mouse escapes
1 M
Q2
Textbook Exercise • Common Multiples of 2 and 3
(a) Write the first five multiples of 2. (b) Write the first five multiples of 3. (c) Write the first two common multiples of 2 and 3. What is their Lowest Common Multiple (LCM)?
[3 Marks]
✅ Step-by-Step Solution & Working
Multiples Analysis:
• (a) Multiples of 2: 2, 4, 6, 8, 10.
• (b) Multiples of 3: 3, 6, 9, 12, 15.
• (c) Common multiples: Numbers appearing in both lists are 6 and 12.
• Lowest Common Multiple (LCM): 6.
• (a) Multiples of 2: 2, 4, 6, 8, 10.
• (b) Multiples of 3: 3, 6, 9, 12, 15.
• (c) Common multiples: Numbers appearing in both lists are 6 and 12.
• Lowest Common Multiple (LCM): 6.
CBSE Step-by-Step Marking Scheme
Multiples of 2 & 3
1 M
Common multiples: 6, 12
1 M
LCM: 6
1 M
Q3
Textbook Exercise • Common Multiples in Venn Diagram
In a two-circle diagram, circle A contains multiples of 4 and circle B contains multiples of 6. (a) Write 4 numbers that belong in the overlapping common region. (b) What is the smallest number in the common region?
[3 Marks]
✅ Step-by-Step Solution & Working
Common Multiples of 4 and 6:
• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48...
• (a) 4 common numbers: 12, 24, 36, 48.
• (b) Smallest common number (LCM): 12.
• Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48...
• Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48...
• (a) 4 common numbers: 12, 24, 36, 48.
• (b) Smallest common number (LCM): 12.
CBSE Step-by-Step Marking Scheme
Common multiples: 12, 24, 36, 48
2 M
Smallest number (LCM): 12
1 M
Q4
Textbook Exercise • Tamarind Seeds Puzzle (LCM + Remainder)
Sunita has some tamarind seeds. When she makes groups of 4, 5, or 6 seeds, 1 seed is always left over. What is the smallest number of seeds Sunita can have?
[3 Marks]
✅ Step-by-Step Solution & Working
LCM Calculation:
1. Find the LCM of 4, 5, and 6:
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60...
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...
- LCM(4, 5, 6) = 60.
2. Since 1 seed is left over in each case, add 1 to the LCM:
Total seeds = 60 + 1 = 61 seeds.
1. Find the LCM of 4, 5, and 6:
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60...
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60...
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...
- LCM(4, 5, 6) = 60.
2. Since 1 seed is left over in each case, add 1 to the LCM:
Total seeds = 60 + 1 = 61 seeds.
CBSE Step-by-Step Marking Scheme
LCM of 4, 5, 6 is 60
2 M
Adding 1 remainder = 61
1 M
Q5
Textbook Exercise • Bangle Arrangements (Factors)
Ammini has 18 bangles. She wants to arrange them in equal rows. List all possible row sizes she can make such that no bangles are left over.
[3 Marks]
✅ Step-by-Step Solution & Working
Factors of 18:
Any arrangement with equal rows must divide 18 completely without remainder.
• 1 row of 18 bangles (1 × 18)
• 2 rows of 9 bangles (2 × 9)
• 3 rows of 6 bangles (3 × 6)
• 6 rows of 3 bangles (6 × 3)
• 9 rows of 2 bangles (9 × 2)
• 18 rows of 1 bangle (18 × 1)
The possible group/row sizes are: 1, 2, 3, 6, 9, and 18.
Any arrangement with equal rows must divide 18 completely without remainder.
• 1 row of 18 bangles (1 × 18)
• 2 rows of 9 bangles (2 × 9)
• 3 rows of 6 bangles (3 × 6)
• 6 rows of 3 bangles (6 × 3)
• 9 rows of 2 bangles (9 × 2)
• 18 rows of 1 bangle (18 × 1)
The possible group/row sizes are: 1, 2, 3, 6, 9, and 18.
CBSE Step-by-Step Marking Scheme
Listing factor pairs
1.5 M
All 6 factor sizes listed
1.5 M
Q6
Textbook Exercise • Factor Tree
Draw two different factor trees for the number 24. Write the prime factorization of 24.
[3 Marks]
✅ Step-by-Step Solution & Working
Factor Trees for 24:
• Tree 1: Start with 24 = 2 × 12 → 12 = 2 × 6 → 6 = 2 × 3.
• Tree 2: Start with 24 = 4 × 6 → 4 = 2 × 2 and 6 = 2 × 3.
• Prime factorization: 24 = 2 × 2 × 2 × 3.
• Tree 1: Start with 24 = 2 × 12 → 12 = 2 × 6 → 6 = 2 × 3.
• Tree 2: Start with 24 = 4 × 6 → 4 = 2 × 2 and 6 = 2 × 3.
• Prime factorization: 24 = 2 × 2 × 2 × 3.
CBSE Step-by-Step Marking Scheme
Tree 1 branches
1 M
Tree 2 branches
1 M
Prime factorization: 2 × 2 × 2 × 3
1 M
Q7
Textbook Exercise • Common Factors of 25 and 35
(a) List all factors of 25. (b) List all factors of 35. (c) What are the common factors of 25 and 35? What is their Highest Common Factor (HCF)?
[3 Marks]
✅ Step-by-Step Solution & Working
Factors Analysis:
• (a) Factors of 25: 1, 5, 25.
• (b) Factors of 35: 1, 5, 7, 35.
• (c) Common factors: 1 and 5.
• Highest Common Factor (HCF): 5.
• (a) Factors of 25: 1, 5, 25.
• (b) Factors of 35: 1, 5, 7, 35.
• (c) Common factors: 1 and 5.
• Highest Common Factor (HCF): 5.
CBSE Step-by-Step Marking Scheme
Factors of 25 & 35
1 M
Common factors: 1, 5
1 M
HCF: 5
1 M
Q8
Textbook Exercise • Tiling Path Problem (HCF)
A garden path is 90 feet long. Sheena wants to tile the path without cutting any tile. She has tiles of sizes 2 feet, 3 feet, and 5 feet. Which of these tile sizes can be used to tile the entire path completely?
[3 Marks]
✅ Step-by-Step Solution & Working
Divisibility Test:
• 90 ÷ 2 = 45 (divides evenly, so 2-foot tiles can be used: 45 tiles).
• 90 ÷ 3 = 30 (divides evenly, so 3-foot tiles can be used: 30 tiles).
• 90 ÷ 5 = 18 (divides evenly, so 5-foot tiles can be used: 18 tiles).
All three tile sizes (2 ft, 3 ft, and 5 ft) can tile the path completely without cutting!
• 90 ÷ 2 = 45 (divides evenly, so 2-foot tiles can be used: 45 tiles).
• 90 ÷ 3 = 30 (divides evenly, so 3-foot tiles can be used: 30 tiles).
• 90 ÷ 5 = 18 (divides evenly, so 5-foot tiles can be used: 18 tiles).
All three tile sizes (2 ft, 3 ft, and 5 ft) can tile the path completely without cutting!
CBSE Step-by-Step Marking Scheme
Divisibility by 2, 3, 5 checked
2 M
Conclusion that all three can be used
1 M
Q9
Textbook Exercise • Prime and Composite Numbers
(a) Define Prime Number and Composite Number. (b) Which is the smallest prime number? (c) Which is the only even prime number? (d) Is 1 a prime number or composite number?
[4 Marks]
✅ Step-by-Step Solution & Working
Definitions and Facts:
• (a) Definitions: A Prime Number has exactly two distinct factors (1 and itself). A Composite Number has more than two factors.
• (b) Smallest prime number: 2.
• (c) Only even prime number: 2.
• (d) Number 1: 1 has only one factor (itself). Therefore, 1 is neither prime nor composite.
• (a) Definitions: A Prime Number has exactly two distinct factors (1 and itself). A Composite Number has more than two factors.
• (b) Smallest prime number: 2.
• (c) Only even prime number: 2.
• (d) Number 1: 1 has only one factor (itself). Therefore, 1 is neither prime nor composite.
CBSE Step-by-Step Marking Scheme
Definitions: Prime & Composite
1 M
Smallest prime: 2
1 M
Even prime: 2
1 M
Number 1 neither prime nor composite
1 M
Q10
Textbook Exercise • Common Multiples of 3, 4, and 6
Find the first two common multiples of 3, 4, and 6. What is their LCM?
[3 Marks]
✅ Step-by-Step Solution & Working
Multiples of 3, 4, 6:
• Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27...
• Multiples of 4: 4, 8, 12, 16, 20, 24, 28...
• Multiples of 6: 6, 12, 18, 24, 30...
• First two common multiples: 12 and 24.
• LCM: 12.
• Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27...
• Multiples of 4: 4, 8, 12, 16, 20, 24, 28...
• Multiples of 6: 6, 12, 18, 24, 30...
• First two common multiples: 12 and 24.
• LCM: 12.
CBSE Step-by-Step Marking Scheme
Lists of multiples
1 M
Common multiples: 12, 24
1 M
LCM: 12
1 M
Q11
Textbook Exercise • Factor Pairs of 36
Write all the factor pairs of 36. How many total factors does 36 have?
[3 Marks]
✅ Step-by-Step Solution & Working
Factor Pairs of 36:
• 1 × 36 = 36
• 2 × 18 = 36
• 3 × 12 = 36
• 4 × 9 = 36
• 6 × 6 = 36
All distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Total number of factors = 9 factors.
• 1 × 36 = 36
• 2 × 18 = 36
• 3 × 12 = 36
• 4 × 9 = 36
• 6 × 6 = 36
All distinct factors: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Total number of factors = 9 factors.
CBSE Step-by-Step Marking Scheme
All 5 factor pairs listed
1.5 M
Total 9 factors identified
1.5 M
Q12
Textbook Exercise • Multiple Game (Meow Game)
In the 'Meow Game', children stand in a circle and count 1, 2, 3... Whenever a number is a multiple of 3 or has 3 in it, the child must say 'Meow!' instead of the number. Write down the first five numbers where children say 'Meow!'.
[2 Marks]
✅ Step-by-Step Solution & Working
Meow Numbers:
• 3 (multiple of 3 and has digit 3) → Meow!
• 6 (multiple of 3) → Meow!
• 9 (multiple of 3) → Meow!
• 12 (multiple of 3) → Meow!
• 13 (has digit 3) → Meow!
First five numbers: 3, 6, 9, 12, 13.
• 3 (multiple of 3 and has digit 3) → Meow!
• 6 (multiple of 3) → Meow!
• 9 (multiple of 3) → Meow!
• 12 (multiple of 3) → Meow!
• 13 (has digit 3) → Meow!
First five numbers: 3, 6, 9, 12, 13.
CBSE Step-by-Step Marking Scheme
Rule application (multiple or contains 3)
1 M
List: 3, 6, 9, 12, 13
1 M
Q13
Textbook Exercise • HCF by Prime Factorization
Find the HCF of 40 and 60 using prime factorization method.
[3 Marks]
✅ Step-by-Step Solution & Working
Prime Factorization:
• 40 = 2 × 2 × 2 × 5.
• 60 = 2 × 2 × 3 × 5.
• Common prime factors = 2 × 2 × 5.
• HCF: 2 × 2 × 5 = 20.
• 40 = 2 × 2 × 2 × 5.
• 60 = 2 × 2 × 3 × 5.
• Common prime factors = 2 × 2 × 5.
• HCF: 2 × 2 × 5 = 20.
CBSE Step-by-Step Marking Scheme
Prime factors of 40 and 60
1.5 M
HCF calculation = 20
1.5 M
Q14
Textbook Exercise • Bells Tolling Together (LCM Word Problem)
Two church bells toll at intervals of 15 minutes and 20 minutes respectively. If they toll together at 8:00 AM, at what time will they next toll together?
[3 Marks]
✅ Step-by-Step Solution & Working
LCM Calculation:
1. Find LCM of 15 and 20:
- Multiples of 15: 15, 30, 45, 60, 75...
- Multiples of 20: 20, 40, 60, 80...
- LCM = 60 minutes = 1 hour.
2. Time of next toll = 8:00 AM + 1 hour = 9:00 AM.
1. Find LCM of 15 and 20:
- Multiples of 15: 15, 30, 45, 60, 75...
- Multiples of 20: 20, 40, 60, 80...
- LCM = 60 minutes = 1 hour.
2. Time of next toll = 8:00 AM + 1 hour = 9:00 AM.
CBSE Step-by-Step Marking Scheme
LCM of 15 and 20 = 60 mins
1.5 M
Next toll time: 9:00 AM
1.5 M
Q15
Textbook Exercise • Co-Prime Numbers
Two numbers are called co-prime if their only common factor is 1. Check whether 8 and 15 are co-prime numbers.
[2 Marks]
✅ Step-by-Step Solution & Working
Co-prime Verification:
• Factors of 8: 1, 2, 4, 8.
• Factors of 15: 1, 3, 5, 15.
• Common factors: Only 1.
• Conclusion: Yes, 8 and 15 are co-prime numbers.
• Factors of 8: 1, 2, 4, 8.
• Factors of 15: 1, 3, 5, 15.
• Common factors: Only 1.
• Conclusion: Yes, 8 and 15 are co-prime numbers.
CBSE Step-by-Step Marking Scheme
Factors listed
1 M
Only common factor 1, affirmative conclusion
1 M
Q16
Textbook Exercise • Divisibility Rule for 3 and 9
(a) State the divisibility rule for 3. (b) Test if 4,572 is divisible by 3. (c) Is 4,572 also divisible by 9?
[3 Marks]
✅ Step-by-Step Solution & Working
Divisibility Tests:
• (a) Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
• (b) Sum of digits of 4,572: 4 + 5 + 7 + 2 = 18. Since 18 is divisible by 3 (18 ÷ 3 = 6), 4,572 is divisible by 3.
• (c) Divisible by 9: The sum of digits is 18. Since 18 is divisible by 9 (18 ÷ 9 = 2), 4,572 is also divisible by 9.
• (a) Rule for 3: A number is divisible by 3 if the sum of its digits is divisible by 3.
• (b) Sum of digits of 4,572: 4 + 5 + 7 + 2 = 18. Since 18 is divisible by 3 (18 ÷ 3 = 6), 4,572 is divisible by 3.
• (c) Divisible by 9: The sum of digits is 18. Since 18 is divisible by 9 (18 ÷ 9 = 2), 4,572 is also divisible by 9.
CBSE Step-by-Step Marking Scheme
Rule for 3 stated
1 M
Sum of digits 18 and divisibility by 3
1 M
Divisibility by 9 verified
1 M
Q17
Textbook Exercise • Multiples between 100 and 150
Find all the multiples of 7 that lie between 100 and 150.
[3 Marks]
✅ Step-by-Step Solution & Working
Division to find range:
• 100 ÷ 7 = 14 with remainder 2. Smallest multiple > 100 is 7 × 15 = 105.
• 150 ÷ 7 = 21 with remainder 3. Largest multiple < 150 is 7 × 21 = 147.
• Multiples: 105, 112, 119, 126, 133, 140, 147.
• 100 ÷ 7 = 14 with remainder 2. Smallest multiple > 100 is 7 × 15 = 105.
• 150 ÷ 7 = 21 with remainder 3. Largest multiple < 150 is 7 × 21 = 147.
• Multiples: 105, 112, 119, 126, 133, 140, 147.
CBSE Step-by-Step Marking Scheme
Range identified
1 M
All 7 multiples listed correctly
2 M
Q18
Textbook Exercise • Factor Tree for 60
Complete a factor tree for 60 starting with 6 and 10. Write down its prime factorization.
[2 Marks]
✅ Step-by-Step Solution & Working
Factor Tree Branches:
• Level 1: 60 = 6 × 10.
• Level 2: 6 splits into 2 × 3; 10 splits into 2 × 5.
• Prime factorization: 60 = 2 × 2 × 3 × 5.
• Level 1: 60 = 6 × 10.
• Level 2: 6 splits into 2 × 3; 10 splits into 2 × 5.
• Prime factorization: 60 = 2 × 2 × 3 × 5.
CBSE Step-by-Step Marking Scheme
Branching steps shown
1 M
Prime factors: 2 × 2 × 3 × 5
1 M
Q19
Textbook Exercise • Even & Odd Numbers Properties
State whether True or False:
(a) The sum of two odd numbers is always even.
(b) The product of two odd numbers is always even.
(c) All even numbers are composite numbers.
[3 Marks]
(a) The sum of two odd numbers is always even.
(b) The product of two odd numbers is always even.
(c) All even numbers are composite numbers.
✅ Step-by-Step Solution & Working
True/False Explanations:
• (a) True: E.g., 3 + 5 = 8 (even).
• (b) False: The product of two odd numbers is always odd (e.g., 3 × 5 = 15).
• (c) False: 2 is an even number, but it is a prime number, not composite.
• (a) True: E.g., 3 + 5 = 8 (even).
• (b) False: The product of two odd numbers is always odd (e.g., 3 × 5 = 15).
• (c) False: 2 is an even number, but it is a prime number, not composite.
CBSE Step-by-Step Marking Scheme
Part (a): True with reason
1 M
Part (b): False with reason
1 M
Part (c): False (counterexample 2)
1 M
Q20
Textbook Exercise • Largest 2-Digit Prime Number
(a) What is the largest two-digit prime number? (b) What is the smallest two-digit composite number?
[2 Marks]
✅ Step-by-Step Solution & Working
Number Identification:
• (a) Largest 2-digit prime: 97 (factors: only 1 and 97).
• (b) Smallest 2-digit composite: 10 (factors: 1, 2, 5, 10).
• (a) Largest 2-digit prime: 97 (factors: only 1 and 97).
• (b) Smallest 2-digit composite: 10 (factors: 1, 2, 5, 10).
CBSE Step-by-Step Marking Scheme
Part (a): 97
1 M
Part (b): 10
1 M
Q21
Textbook Exercise • Step Measure LCM
Two runners start running on a circular track together. Runner A completes a lap in 40 seconds, while Runner B completes a lap in 50 seconds. After how many seconds will they meet again at the starting point?
[2 Marks]
✅ Step-by-Step Solution & Working
LCM of 40 and 50:
• Multiples of 40: 40, 80, 120, 160, 200, 240...
• Multiples of 50: 50, 100, 150, 200, 250...
• LCM = 200 seconds (or 3 minutes and 20 seconds).
They will meet again after 200 seconds.
• Multiples of 40: 40, 80, 120, 160, 200, 240...
• Multiples of 50: 50, 100, 150, 200, 250...
• LCM = 200 seconds (or 3 minutes and 20 seconds).
They will meet again after 200 seconds.
CBSE Step-by-Step Marking Scheme
LCM calculation
1 M
200 seconds answer
1 M
Q22
Textbook Exercise • Perfect Numbers
A number is called a 'perfect number' if the sum of all its proper factors (excluding itself) equals the number. Show that 6 is a perfect number.
[2 Marks]
✅ Step-by-Step Solution & Working
Factors of 6:
• Factors of 6 are 1, 2, 3, and 6.
• Proper factors (excluding 6) = 1, 2, 3.
• Sum of proper factors = 1 + 2 + 3 = 6.
Since the sum equals the number itself, 6 is a perfect number.
• Factors of 6 are 1, 2, 3, and 6.
• Proper factors (excluding 6) = 1, 2, 3.
• Sum of proper factors = 1 + 2 + 3 = 6.
Since the sum equals the number itself, 6 is a perfect number.
CBSE Step-by-Step Marking Scheme
Proper factors listed: 1, 2, 3
1 M
Sum = 6 verified
1 M
Q23
Textbook Exercise • Divisibility Rule for 6
A number is divisible by 6 if it is divisible by both 2 and 3. Is 3,426 divisible by 6? Show your working.
[3 Marks]
✅ Step-by-Step Solution & Working
Test for 6:
1. Divisibility by 2: The last digit is 6 (even), so 3,426 is divisible by 2.
2. Divisibility by 3: Sum of digits = 3 + 4 + 2 + 6 = 15. Since 15 is divisible by 3, 3,426 is divisible by 3.
3. Conclusion: Since it is divisible by both 2 and 3, 3,426 is divisible by 6.
1. Divisibility by 2: The last digit is 6 (even), so 3,426 is divisible by 2.
2. Divisibility by 3: Sum of digits = 3 + 4 + 2 + 6 = 15. Since 15 is divisible by 3, 3,426 is divisible by 3.
3. Conclusion: Since it is divisible by both 2 and 3, 3,426 is divisible by 6.
CBSE Step-by-Step Marking Scheme
Test for 2 passed
1 M
Test for 3 passed
1 M
Conclusion for 6
1 M
Q24
Textbook Exercise • Square Numbers as Multiples
Write the first five square numbers and list the number of factors each has. What is unique about the number of factors of square numbers?
[3 Marks]
✅ Step-by-Step Solution & Working
Square Numbers & Factor Count:
• 1² = 1 (1 factor: 1) → Odd count.
• 2² = 4 (3 factors: 1, 2, 4) → Odd count.
• 3² = 9 (3 factors: 1, 3, 9) → Odd count.
• 4² = 16 (5 factors: 1, 2, 4, 8, 16) → Odd count.
• 5² = 25 (3 factors: 1, 5, 25) → Odd count.
• Unique Property: All square numbers have an odd number of factors, because the square root pairs with itself. All other numbers have an even number of factors.
• 1² = 1 (1 factor: 1) → Odd count.
• 2² = 4 (3 factors: 1, 2, 4) → Odd count.
• 3² = 9 (3 factors: 1, 3, 9) → Odd count.
• 4² = 16 (5 factors: 1, 2, 4, 8, 16) → Odd count.
• 5² = 25 (3 factors: 1, 5, 25) → Odd count.
• Unique Property: All square numbers have an odd number of factors, because the square root pairs with itself. All other numbers have an even number of factors.
CBSE Step-by-Step Marking Scheme
First 5 square numbers listed
1 M
Factor counts identified
1 M
Odd number of factors property explained
1 M
🌟 NEP 2020 Competency-Based Case Study
NEP 2020 Competency Case: Be My Multiple, I'll be Your Factor
A practical scenario involving Be My Multiple, I'll be Your Factor in everyday life and community contexts.
Analytical Task: Analyze the quantitative relationships and state the conclusion.
Evaluation & Model Answer:
Apply the step-by-step formulas and concepts mastered in this chapter.
Rubric: 1M formula + 1M working + 1M answer