NCERT Solutions Class 9 Maths Chapter 11 — The World of Algorithms#

Chapter 11 (Ganita Manjari Part II) introduces algorithms — precise, step-by-step procedures for solving a problem. Starting from the column-addition method, it builds algorithms for listing divisors and finding the gcd, improves them step by step, and ends with Euclid’s subtraction algorithm and Āryabhaṭa’s division algorithm, which are fast even for very large numbers.

exercise set 11.1 exercise set 11.2 exercise set 11.3 end-of-chapter exercises

Exercises#

  • Exercise Set 11.1 — Following the addition algorithm exactly; numbers of different lengths, carries and the final step (5 questions)
  • Exercise Set 11.2 — Comparing sorted lists, an algorithm for lcm, divisors in pairs (3 questions)
  • Exercise Set 11.3 — Scanning divisors in reverse order (2 questions)
  • End-of-Chapter Exercises — gcd by Āryabhaṭa’s division algorithm, algorithms for primes, prime divisors and prime factorisation (5 questions)

What you will learn#

  • What an algorithm is, starting from the familiar addition algorithm.
  • Finding all divisors of a number, and the gcd of two numbers.
  • Euclid’s algorithm and Āryabhaṭa’s division method for the gcd.
  • Writing algorithms for primes, prime factorisation and the lcm.

Key formulas and results#

  • $\gcd(m, n) = \gcd(n, m \bmod n)$ — the step that makes the division algorithm fast.
  • $\gcd(m, n) \times \text{lcm}(m, n) = m \times n$.

Read and revise#

Frequently asked questions#

How many exercises are in Class 9 Maths Chapter 11?
Three exercise sets — 11.1 (5 questions), 11.2 (3 questions) and 11.3 (2 questions) — plus 5 end-of-chapter exercises. Every question is solved step by step here.
What makes a list of steps an algorithm?
Every step must be precise, the process must finish after a finite number of steps, and it must give the correct result for every allowed input.

Quick links