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Gyaan Maths
CBSE · Class 6-12
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CBSE Maths · Class 9

Chapter 11: The World of Algorithms

Name: ________________________
Date: ______________
Marks: ____ / 6

An algorithm is a step-by-step recipe. Explore ancient and modern algorithms for arithmetic and number theory.

Questions

  1. HCF of 5656 and 2424 by Euclid.
  2. HCF of 100100 and 7575.
  3. HCF of 180180 and 150150.
  4. How many steps of Euclid to reach gcd⁡(21,14)\gcd(21, 14)?
  5. Is "pick any number and shout" an algorithm?
  6. HCF of two consecutive integers, say 1414 and 1515?

Extra Practice (Optional)

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Answer Key (For Teachers)

  1. Answer: 88
    Working: 56=2⋅24+856 = 2\cdot 24 + 8; 24=3⋅8+024 = 3\cdot 8 + 0.
  2. Answer: 2525
    Working: 100=1⋅75+25100 = 1\cdot 75 + 25; 75=3⋅25+075 = 3\cdot 25 + 0.
  3. Answer: 3030
    Working: 180=1⋅150+30180 = 1\cdot 150 + 30; 150=5⋅30+0150 = 5\cdot 30 + 0.
  4. Answer: 22 steps
    Working: 21=1⋅14+721=1\cdot 14+7; 14=2⋅7+014=2\cdot 7+0.
  5. Answer: No
    Working: Ambiguous — not deterministic.
  6. Answer: 11
    Working: Any common divisor of n,n+1n, n+1 divides 11.
Gyaan Maths · CBSE Class 9 · Chapter 11
Gyaan Maths — CBSE Class 6-12, built for board-toppers.
v1.1 · Sept 2026