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Prime Factorisation

Class 6 Maths · Chapter 5: Prime Time · NCERT Ganita Prakash section 5.4

Learn

Every composite number can be broken into prime building blocks. 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5. This is the prime factorisation of 60.

A factor tree helps. Split 60 any way you like, for example 6 × 10, then split again: 6 = 2 × 3 and 10 = 2 × 5. You still end with 2, 2, 3, 5. Whichever way you start, the primes are always the same!

Prime factorisations make comparing easy. 36 = 2 × 2 × 3 × 3 and 35 = 5 × 7 share no prime, so 36 and 35 are co-prime. 36 and 60 share 2, 2, 3, so 2 × 2 × 3 = 12 is their biggest common factor.

shared: 2 × 2 × 3 = 12

Explore: grow factor trees. Tap a number that is not prime and choose how to split it.

  1. Split 60 until every branch ends in a prime.
  2. Now a new tree: break 72 into primes.

Remember

  • Prime factorisation: write a number as a product of primes only (60 = 2 × 2 × 3 × 5).
  • However you split, you get the same primes. Shared primes show common factors.

Quick check

Which is the prime factorisation of 24?

  1. 4 × 6
  2. 2 × 12
  3. 2 × 2 × 2 × 3
  4. 3 × 8
Answer

2 × 2 × 2 × 3. Only 2 × 2 × 2 × 3 uses primes alone. 4, 6, 12 and 8 are not prime.

Think about it

What is the smallest number whose prime factorisation has four 2s and one 3?

One answer

2 × 2 × 2 × 2 × 3 = 48. (There is only one such number, so it is also the smallest.)

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.