Prime factorisation
- CBSE · NCERT Class 10, Ch 1 Real Numbers
Prime factorisation means writing a number as a product of prime numbers only, such as 60 = 2 × 2 × 3 × 5.
To find a number's prime factors, keep dividing by primes until only 1 is left. Start with 2, then 3, then 5, and so on. The primes you divided by are the prime factors. Powers keep the answer short: 2 × 2 × 3 × 5 is written 2² × 3 × 5.
The chapter uses this method to find the HCF and LCM of numbers. The Fundamental Theorem of Arithmetic says the factorisation of a number is always the same.
A small example
Find the smallest number that, when increased by 17, is exactly divisible by both 520 and 468. First factorise each number:
- 520 = 2³ × 5 × 13
- 468 = 2² × 3² × 13
The LCM takes the highest power of every prime: 2³ × 3² × 5 × 13 = 4680. The number we want is 17 less, so 4680 - 17 = 4663.
Where marks go
This is Question 21(A) of CBSE's 2026-27 Maths Basic sample paper, worth 2 marks. The board's marking scheme gives 1 mark for the two factorisations. It gives half a mark for the LCM, 4680, and half a mark for the final 4663.
So the factorisations carry half the marks by themselves. A correct final number is only the last half mark of the 2. Our guide on how step marking splits a short answer shows the same pattern in other questions.
Sources
Facts last checked against these sources on 30 September 2026.
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