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…

By Syllab.in · Updated Jun 14, 2026

Key Questions Covered:

Find the next three numbers in the pattern: 2, 6, 18, 54, ...
Check if 256 is divisible by 8 without performing division.
Is 4527 divisible by 3? Use the divisibility rule.
Find HCF (Highest Common Factor) of 24 and 36 using the Euclidean algorithm.
Check if 144 is a perfect square. If yes, find its square root.
Find the LCM (Least Common Multiple) of 12 and 18.
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
Find the next three numbers in the pattern: 2, 6, 18, 54,…	✓ Solved
Check if 256 is divisible by 8 without performing division.	✓ Solved
Is 4527 divisible by 3? Use the divisibility rule.	✓ Solved
Find HCF (Highest Common Factor) of 24 and 36 using the E…	✓ Solved
Check if 144 is a perfect square. If yes, find its square…	✓ Solved
Find the LCM (Least Common Multiple) of 12 and 18.	✓ Solved

Showing 6 of 8 questions

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

Showing 6 of 8 questions. Visit the full page for complete solutions.