Number Play — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Number Play" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Number Play" — 8 important questions with detailed answers for CBSE board exam prep…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 6 Mathematics — Number Play. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Number Play — All 8 Questions Solved
Q1. Use the digits 2, 3, and 7 to form the smallest and largest 3-digit numbers.
Step 1: List the digits available: 2, 3, 7
Step 2: To form the smallest 3-digit number, arrange digits in ascending order
Smallest number: 237
Step 3: To form the largest 3-digit number, arrange digits in descending order
Largest number: 732
Step 4: Verify
237 < 732 ✓
Answer: Smallest = 237, Largest = 732
Q2. Find the magic number where 18 × magic number = 18. What is the magic number?
We need to find the number that when multiplied by 18 gives 18.
Step 1: Set up the equation
18 × magic number = 18
Step 2: Divide both sides by 18
magic number = 18 ÷ 18
magic number = 1
Step 3: Verify: 18 × 1 = 18 ✓
Answer: The magic number is 1
Q3. What is special about the number 1 in multiplication?
Step 1: Test multiplication with 1
5 × 1 = 5
10 × 1 = 10
100 × 1 = 100
Step 2: Observe the pattern
When any number is multiplied by 1, the result is that same number
Step 3: Name this property
This is called the multiplicative identity property or multiplication by 1
Answer: 1 is the multiplicative identity. When any number is multiplied by 1, the result is the number itself. The number remains unchanged.
Q4. Is 51 divisible by 3? Show your working using divisibility rules.
To check divisibility by 3, use the rule: A number is divisible by 3 if the sum of its digits is divisible by 3.
Step 1: Find the sum of digits in 51
Digits: 5 and 1
Sum = 5 + 1 = 6
Step 2: Check if 6 is divisible by 3
6 ÷ 3 = 2 (exactly, no remainder)
Yes, 6 is divisible by 3
Step 3: Verify by dividing 51 by 3
51 ÷ 3 = 17
Answer: Yes, 51 is divisible by 3 because the sum of its digits (5 + 1 = 6) is divisible by 3. Also, 51 = 3 × 17
Q5. A number when divided by 5 leaves no remainder. What must be its last digit?
Use the divisibility rule for 5: A number is divisible by 5 if its last digit is 0 or 5.
Step 1: Remember the rule for divisibility by 5
If a number ends in 0 or 5, it can be divided by 5 evenly
Step 2: Explain why
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, ...
Notice all end in either 0 or 5
Step 3: Any number that leaves no remainder when divided by 5 must end in 0 or 5
Example: 25 ÷ 5 = 5, 40 ÷ 5 = 8
Answer: The last digit must be either 0 or 5
Q6. Using the digits 1, 2, 3 (each exactly once), form a number divisible by 4.
To check divisibility by 4: A number is divisible by 4 if the last two digits form a number divisible by 4.
Step 1: List all possible 3-digit numbers using 1, 2, 3 (each once)
123, 132, 213, 231, 312, 321
Step 2: Check the last two digits of each for divisibility by 4
123: last two digits = 23. Is 23 divisible by 4? 23 ÷ 4 = 5.75 (NO)
132: last two digits = 32. Is 32 divisible by 4? 32 ÷ 4 = 8 (YES) ✓
213: last two digits = 13. Is 13 divisible by 4? 13 ÷ 4 = 3.25 (NO)
231: last two digits = 31. Is 31 divisible by 4? 31 ÷ 4 = 7.75 (NO)
312: last two digits = 12. Is 12 divisible by 4? 12 ÷ 4 = 3 (YES) ✓
321: last two digits = 21. Is 21 divisible by 4? 21 ÷ 4 = 5.25 (NO)
Step 3: Valid answers
132 and 312 are both divisible by 4
Answer: 132 or 312 (or both). For example, 132 ÷ 4 = 33
Q7. What is the HCF (Highest Common Factor) of 24 and 36?
The HCF is the largest number that divides both numbers evenly.
Step 1: Find all factors of 24
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Step 2: Find all factors of 36
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Step 3: Find common factors (numbers in both lists)
Common factors: 1, 2, 3, 4, 6, 12
Step 4: Identify the highest common factor
HCF = 12
Step 5: Verify
24 ÷ 12 = 2 ✓
36 ÷ 12 = 3 ✓
Answer: The HCF of 24 and 36 is 12
Q8. Find the LCM (Lowest Common Multiple) of 8 and 12.
The LCM is the smallest number that is a multiple of both numbers.
Step 1: List multiples of 8
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
Step 2: List multiples of 12
Multiples of 12: 12, 24, 36, 48, 60, 72, ...
Step 3: Find common multiples (numbers in both lists)
Common multiples: 24, 48, 72, ...
Step 4: Identify the lowest common multiple
LCM = 24
Step 5: Verify
24 ÷ 8 = 3 ✓
24 ÷ 12 = 2 ✓
Answer: The LCM of 8 and 12 is 24
Number Play — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. What are all the factors of 18?
- A. 1, 2, 3, 6, 9, 18
- B. 1, 2, 3, 4, 6, 9, 18
- C. 1, 2, 3, 9, 18
- D. 1, 2, 3, 6, 18
Answer: A. 1, 2, 3, 6, 9, 18 — Factors are numbers that divide the given number exactly without leaving a remainder. For 18, these are 1, 2, 3, 6, 9, and 18.
MCQ 2. Which of the following is NOT a multiple of 7?
- A. 21
- B. 35
- C. 42
- D. 50
Answer: D. 50 — Multiples of 7 are numbers obtained by multiplying 7 by an integer. 50 is not divisible by 7 (7 x 7 = 49, 7 x 8 = 56), so it is not a multiple of 7.
MCQ 3. Which of the following is a prime number?
- A. 9
- B. 15
- C. 23
- D. 27
Answer: C. 23 — A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 23 is only divisible by 1 and 23.
MCQ 4. What is the smallest composite number?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: D. 4 — A composite number is a natural number greater than 1 that has more than two factors (1, itself, and at least one other factor). 4 has factors 1, 2, and 4, making it the smallest composite number.
MCQ 5. Which of the following numbers is divisible by 5?
- A. 124
- B. 305
- C. 412
- D. 531
Answer: B. 305 — A number is divisible by 5 if its last digit is either 0 or 5. In 305, the last digit is 5, so it is divisible by 5.
MCQ 6. What is the smallest digit that can be placed in the blank space of 7_2 to make the number divisible by 3?
- A. 0
- B. 1
- C. 2
- D. 3
Answer: A. 0 — A number is divisible by 3 if the sum of its digits is divisible by 3. The current sum of known digits is 7+2=9. If we place 0 in the blank, the sum becomes 9+0=9, which is divisible by 3. Thus, 0 is the smallest digit.
MCQ 7. Find the Highest Common Factor (HCF) of 24 and 36.
- A. 6
- B. 8
- C. 12
- D. 18
Answer: C. 12 — The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The highest number common to both lists is 12.
MCQ 8. Find the Least Common Multiple (LCM) of 8, 12, and 16.
- A. 24
- B. 32
- C. 48
- D. 64
Answer: C. 48 — The multiples of 8 are 8, 16, 24, 32, 40, 48... The multiples of 12 are 12, 24, 36, 48... The multiples of 16 are 16, 32, 48... The smallest number common to all these lists is 48.
MCQ 9. Which of the following numbers is divisible by 11?
- A. 1331
- B. 1234
- C. 1452
- D. 1563
Answer: A. 1331 — A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11. For 1331, (1+3) - (3+1) = 4 - 4 = 0, so it is divisible by 11.
MCQ 10. Which of the following pairs of numbers are co-prime?
- A. (12, 18)
- B. (15, 20)
- C. (8, 9)
- D. (7, 14)
Answer: C. (8, 9) — Co-prime numbers (or relatively prime numbers) are two numbers that have no common factors other than 1. The HCF of 8 and 9 is 1, so they are co-prime.
MCQ 11. What is the greatest number that will divide 120 and 192 exactly?
- A. 8
- B. 12
- C. 16
- D. 24
Answer: D. 24 — This question asks for the Highest Common Factor (HCF) of 120 and 192. By prime factorization, 120 = 2³ × 3 × 5 and 192 = 2⁶ × 3. The HCF is 2³ × 3 = 8 × 3 = 24.
MCQ 12. Three bells ring at intervals of 10, 15, and 20 minutes respectively. If they ring together at 10:00 AM, at what time will they next ring together?
- A. 10:30 AM
- B. 11:00 AM
- C. 11:30 AM
- D. 12:00 PM
Answer: B. 11:00 AM — To find when they will ring together again, we need to find the Least Common Multiple (LCM) of 10, 15, and 20. LCM(10, 15, 20) = 60. So, they will ring together after 60 minutes, which is at 11:00 AM.
MCQ 13. Which of the following statements is true?
- A. Every multiple of a number is smaller than or equal to the number itself.
- B. Every factor of a number is greater than or equal to the number itself.
- C. 1 is neither a prime nor a composite number.
- D. All prime numbers are odd.
Answer: C. 1 is neither a prime nor a composite number. — 1 is a special number that has only one factor (itself), so it does not fit the definition of a prime number (exactly two factors) or a composite number (more than two factors). The other statements are false.
MCQ 14. A number is divisible by 6 if it is divisible by:
- A. 2 and 3
- B. 2 and 4
- C. 3 and 4
- D. 2 and 5
Answer: A. 2 and 3 — For a number to be divisible by 6, it must be divisible by both 2 and 3, because 2 and 3 are co-prime factors whose product is 6.
MCQ 15. The HCF of two numbers is 6 and their LCM is 72. If one of the numbers is 18, what is the other number?
- A. 12
- B. 18
- C. 24
- D. 36
Answer: C. 24 — For any two numbers, the product of their HCF and LCM is equal to the product of the numbers themselves. So, 6 × 72 = 18 × other number. This gives 432 = 18 × other number. Dividing 432 by 18 gives 24 as the other number.
MCQ 16. What is the smallest prime number?
- A. 0
- B. 1
- C. 2
- D. 3
Answer: C. 2 — A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. The number 2 is the smallest prime number.
MCQ 17. Which of the following numbers is a multiple of 9?
- A. 49
- B. 54
- C. 61
- D. 70
Answer: B. 54 — A number is a multiple of 9 if the sum of its digits is divisible by 9. For 54, the sum of digits is 5+4=9, which is divisible by 9.
MCQ 18. How many factors does the number 15 have?
- A. 2
- B. 3
- C. 4
- D. 5
Answer: C. 4 — The factors of 15 are the numbers that divide 15 exactly. These are 1, 3, 5, and 15, making a total of 4 factors.
MCQ 19. Which of these numbers is divisible by both 2 and 5?
- A. 12
- B. 25
- C. 30
- D. 43
Answer: C. 30 — A number is divisible by 2 if it's even (ends in 0, 2, 4, 6, 8) and divisible by 5 if it ends in 0 or 5. Only 30 ends in 0, satisfying both conditions.
MCQ 20. What is the HCF (Highest Common Factor) of 12 and 18?
- A. 2
- B. 3
- C. 6
- D. 12
Answer: C. 6 — Factors of 12 are 1, 2, 3, 4, 6, 12. Factors of 18 are 1, 2, 3, 6, 9, 18. The highest common factor is 6.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.