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Gyaan Maths
CBSE · Class 6-10
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CBSE Maths · Class 8

Chapter 16: Playing with Numbers

Name: ________________________
Date: ______________
Marks: ____ / 10

General form of a number; divisibility tests; puzzles with digits.

Questions

  1. General form of 8585.
  2. Prove ab+baab + ba is always divisible by 1111.
  3. Is 8530585305 divisible by 99?
  4. Divisibility test: 27482748 by 1111.
  5. Test: 918918 by 99.
  6. Test: 624624 by 44.
  7. Test: 205205 by 55.
  8. If 2A52A5 is divisible by 99, find AA.
  9. Sum of any three-digit palindrome divisible by ___?
  10. Verify: 37×3=11137 \times 3 = 111 (a repunit).

Extra Practice (Optional)

  • Prove abc−cbaabc-cba is divisible by 9999.
  • Digit sum test for 4738547385 by 33.
  • Is 1010110101 divisible by 33?

Answer Key (For Teachers)

  1. Answer: a=8,b=5a=8, b=5.
    Working: 10⋅8+510\cdot 8+5.
  2. Answer: Proved.
    Working: (10a+b)+(10b+a)=11(a+b)(10a+b)+(10b+a) = 11(a+b).
  3. Answer: No.
    Working: Digit sum =21= 21, not divisible by 99.
  4. Answer: No.
    Working: Alt sum: 2−7+4−8=−92-7+4-8 = -9.
  5. Answer: Yes.
    Working: Digit sum =18= 18.
  6. Answer: Yes.
    Working: Last 22 digits 24/424 / 4.
  7. Answer: Yes.
    Working: Last digit 55.
  8. Answer: A=2A = 2
    Working: Digit sum 2+A+5=7+A2 + A + 5 = 7 + A; multiple of 99 nearest is 99 or 1818.
  9. Answer: 1111 (often).
    Working: Some palindromes like 121121 are divisible by 1111.
  10. Answer: 111111
    Working: Multiplication.
Gyaan Maths · CBSE Class 8 · Chapter 16
Gyaan Maths — CBSE Class 6-10, built for board-toppers.
v1.1 · Feb 2026