Procedure

Prime factorisation

Arithmetic • Number System • Factors and Divisors

Statement

Every integer

n > 1

has a unique factorisation

n = p_{1}^{e_{1}} p_{2}^{e_{2}} \dots p_{k}^{e_{k}}

with

p_{i}

prime.

How to use it

Write

360

as a product of primes.

Step-by-step

1
$360 = 2 \times 180 = 2^{2} \times 90 = 2^{3} \times 45$
Why: Strip all factors of $2$ first.
2
$45 = 3^{2} \times 5$
3
$360 = 2^{3} \times 3^{2} \times 5$

Answer

2^{3} \times 3^{2} \times 5

Watch out

The number of divisors is

(e_{1} + 1) (e_{2} + 1) \dots

, not

e_{1} e_{2} \dots

Also known as

factor tree, express as product of primes