Number Play — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 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 7 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 7 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. Find the next three numbers in the pattern: 2, 6, 18, 54, ...
Step 1: Identify the pattern by finding the relationship between consecutive terms:
6 ÷ 2 = 3
18 ÷ 6 = 3
54 ÷ 18 = 3
Step 2: The pattern multiplies by 3 each time (geometric progression with ratio 3).
Step 3: Find next three terms:
Next term: 54 × 3 = 162
Next term: 162 × 3 = 486
Next term: 486 × 3 = 1458
Answer: 162, 486, 1458
Q2. Check if 256 is divisible by 8 without performing division.
Step 1: Apply divisibility rule for 8:
A number is divisible by 8 if its last three digits are divisible by 8.
Step 2: Last three digits of 256 are: 256
Step 3: Check if 256 is divisible by 8:
256 ÷ 8 = 32 (exactly)
So yes, 256 is divisible by 8.
Step 4: Verify using the rule:
256 = 200 + 56
We need to check just 256.
8 × 32 = 256 ✓
Answer: Yes, 256 is divisible by 8.
Q3. Is 4527 divisible by 3? Use the divisibility rule.
Step 1: Divisibility rule for 3:
A number is divisible by 3 if the sum of its digits is divisible by 3.
Step 2: Find sum of digits of 4527:
4 + 5 + 2 + 7 = 18
Step 3: Check if 18 is divisible by 3:
18 ÷ 3 = 6 (exactly)
Yes, 18 is divisible by 3.
Step 4: Therefore, 4527 is divisible by 3.
Verify: 4527 ÷ 3 = 1509 ✓
Answer: Yes, 4527 is divisible by 3 (since sum of digits = 18, which is divisible by 3).
Q4. Find HCF (Highest Common Factor) of 24 and 36 using the Euclidean algorithm.
Step 1: Apply Euclidean algorithm (repeated division):
36 = 24 × 1 + 12
Step 2: Replace larger number with divisor, divisor with remainder:
24 = 12 × 2 + 0
Step 3: When remainder is 0, the divisor is the HCF:
HCF(24, 36) = 12
Step 4: Verify by listing factors:
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Common factors: 1, 2, 3, 4, 6, 12
Highest common factor: 12 ✓
Answer: HCF(24, 36) = 12
Q5. Check if 144 is a perfect square. If yes, find its square root.
Step 1: A perfect square is a number that can be expressed as the product of an integer with itself.
Step 2: Try to find the square root:
√144 = ?
We need to find a number that when multiplied by itself gives 144.
Step 3: Check:
12 × 12 = 144 ✓
Step 4: Therefore, 144 is a perfect square.
√144 = 12
Answer: Yes, 144 is a perfect square. √144 = 12
Q6. Find the LCM (Least Common Multiple) of 12 and 18.
Step 1: Find the prime factorization of each number:
12 = 2² × 3
18 = 2 × 3²
Step 2: LCM is the product of highest powers of all prime factors:
Highest power of 2: 2²
Highest power of 3: 3²
Step 3: Calculate LCM:
LCM(12, 18) = 2² × 3² = 4 × 9 = 36
Step 4: Verify:
12 × 3 = 36 ✓ (36 is a multiple of 12)
18 × 2 = 36 ✓ (36 is a multiple of 18)
Answer: LCM(12, 18) = 36
Q7. Find the pattern and write the next term: 1, 1, 2, 3, 5, 8, 13, ...
Step 1: Identify the pattern by examining differences and relationships:
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
Step 2: This is the Fibonacci sequence, where each term is the sum of the two previous terms.
Formula: aₙ = aₙ₋₁ + aₙ₋₂
Step 3: Find the next term:
8 + 13 = 21
Answer: The next term is 21. This is the Fibonacci sequence where each number is the sum of the previous two numbers.
Q8. Is 97 a prime number? Justify your answer.
Step 1: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Step 2: To check if 97 is prime, test divisibility by prime numbers up to √97 ≈ 9.8
Prime numbers to test: 2, 3, 5, 7
Step 3: Test each:
97 ÷ 2 = 48.5 (not divisible)
97 ÷ 3 = 32.33... (not divisible)
97 ÷ 5 = 19.4 (not divisible)
97 ÷ 7 = 13.857... (not divisible)
Step 4: Since 97 is not divisible by any prime number up to √97, it is prime.
Answer: Yes, 97 is a prime number. It has no divisors other than 1 and 97.
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. Which of the following numbers is divisible by 2?
- A. 345
- B. 678
- C. 109
- D. 213
Answer: B. 678 — A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, 8). 678 ends with 8, which is an even digit.
MCQ 2. Identify the number that is divisible by 5.
- A. 123
- B. 456
- C. 780
- D. 912
Answer: C. 780 — A number is divisible by 5 if its last digit is either 0 or 5. 780 ends with 0, making it divisible by 5.
MCQ 3. Which of these numbers is divisible by 3?
- A. 257
- B. 341
- C. 516
- D. 824
Answer: C. 516 — A number is divisible by 3 if the sum of its digits is divisible by 3. For 516, the sum of digits is 5 + 1 + 6 = 12, which is divisible by 3.
MCQ 4. Find the number that is divisible by 9.
- A. 1234
- B. 5678
- C. 2736
- D. 9012
Answer: C. 2736 — A number is divisible by 9 if the sum of its digits is divisible by 9. For 2736, the sum of digits is 2 + 7 + 3 + 6 = 18, which is divisible by 9.
MCQ 5. Which of the following numbers is divisible by 6?
- A. 433
- B. 528
- C. 617
- D. 701
Answer: B. 528 — A number is divisible by 6 if it is divisible by both 2 and 3. 528 is even (divisible by 2) and the sum of its digits (5+2+8=15) is divisible by 3.
MCQ 6. Which number is divisible by 4?
- A. 134
- B. 258
- C. 472
- D. 690
Answer: C. 472 — A number is divisible by 4 if the number formed by its last two digits is divisible by 4. For 472, the last two digits form 72, and 72 is divisible by 4 (72 = 4 × 18).
MCQ 7. Which of the following numbers is divisible by 11?
- A. 1232
- B. 2345
- C. 3456
- D. 4567
Answer: A. 1232 — 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 1232, (2+2) - (3+1) = 4 - 4 = 0.
MCQ 8. If 72X is divisible by 9, what is the value of X?
- A. 1
- B. 3
- C. 6
- D. 9
Answer: D. 9 — For 72X to be divisible by 9, the sum of its digits (7 + 2 + X) must be divisible by 9. So, 9 + X must be a multiple of 9. Among the given options, X = 9 makes the sum 18, which is divisible by 9.
MCQ 9. Which of the following is a multiple of 7?
- A. 24
- B. 32
- C. 49
- D. 57
Answer: C. 49 — A multiple of 7 is a number that can be obtained by multiplying 7 by an integer. 49 is 7 multiplied by 7.
MCQ 10. Which number is a factor of 56?
- A. 3
- B. 5
- C. 8
- D. 9
Answer: C. 8 — A factor of 56 is a number that divides 56 exactly, leaving no remainder. 56 divided by 8 is 7, with no remainder.
MCQ 11. How many factors does the number 36 have?
- A. 6
- B. 7
- C. 8
- D. 9
Answer: D. 9 — The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. Counting them gives a total of 9 factors.
MCQ 12. Which of these is a common factor of 24 and 30?
- A. 4
- B. 5
- C. 6
- D. 8
Answer: C. 6 — Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30. The common factors are 1, 2, 3, 6. Among the options, 6 is a common factor.
MCQ 13. The sum of two factors of 40 is 13. What are these two factors?
- A. (1, 12)
- B. (2, 11)
- C. (4, 9)
- D. (5, 8)
Answer: D. (5, 8) — The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. We need to find a pair that sums to 13. The pair (5, 8) sums to 13.
MCQ 14. Which of the following is a prime number?
- A. 4
- B. 9
- C. 13
- D. 15
Answer: C. 13 — A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. 13 has only 1 and 13 as its factors.
MCQ 15. Identify the composite number from the given options.
- A. 2
- B. 7
- C. 11
- D. 21
Answer: D. 21 — A composite number is a natural number greater than 1 that is not prime. 21 has factors 1, 3, 7, and 21, so it is a composite number.
MCQ 16. What is the prime factorization of 60?
- A. 2 x 3 x 10
- B. 2² x 3 x 5
- C. 2 x 5 x 6
- D. 3² x 2 x 5
Answer: B. 2² x 3 x 5 — To find the prime factorization of 60, we break it down into its prime factors: 60 = 2 x 30 = 2 x 2 x 15 = 2 x 2 x 3 x 5 = 2² x 3 x 5.
MCQ 17. Which of the following pairs of numbers is co-prime?
- A. (6, 9)
- B. (10, 15)
- C. (14, 21)
- D. (16, 25)
Answer: D. (16, 25) — Two numbers are co-prime (or relatively prime) if their greatest common factor (HCF) is 1. The HCF of 16 and 25 is 1, as they share no common prime factors.
MCQ 18. What is the smallest prime factor of the number 119?
- A. 3
- B. 7
- C. 11
- D. 13
Answer: B. 7 — To find the smallest prime factor, we test prime numbers starting from 2. 119 is not divisible by 2, 3, or 5. 119 divided by 7 is 17, so 7 is a prime factor and the smallest one.
MCQ 19. What is the HCF (Highest Common Factor) of 12 and 18?
- A. 2
- B. 3
- C. 6
- D. 9
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.
MCQ 20. Find the LCM (Least Common Multiple) of 6 and 8.
- A. 12
- B. 18
- C. 24
- D. 48
Answer: C. 24 — Multiples of 6 are 6, 12, 18, 24, 30... Multiples of 8 are 8, 16, 24, 32... The least common multiple is 24.
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.