Question

Find the prime factorisation of 120.

Answer 1

Hint: Here, to find the prime factorisation of 120 we need to write 120 into multiples of prime factors.

Complete step-by-step answer:

As we know, 120 can be written as $6 \times 20$.
We know that 6 and 20 are not prime factors, so let us split 6 and 20 as well into prime factors till all the factors are prime i.e..,
\[
   \Rightarrow 120 = 6 \times 20 \\
   \Rightarrow 120 = 2 \times 3 \times 4 \times 5\left[ {\because 6 = 2 \times 3,20 = 4 \times 5} \right] \\
   \Rightarrow 120 = 2 \times 3 \times {2^2} \times 5\left[ {\because 4 = {2^2}} \right] \\
   \Rightarrow 120 = {2^3} \times 3 \times 5 \\
 \]
As we know, 2, 3 and 5 are prime factors. Hence, the prime factorisation on 120 is ${2^3} \times 3 \times 5$.

Note: Prime factorisation means writing a number into multiples of prime numbers. Factor of a number could be any number which can divide it. But prime factor means those factors which are prime.