Factors, GCD & LCM

Prime factorisation, all factors, the GCD and LCM of several numbers, and a quick prime check.

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Number

Whole number

Any whole number from 1 up to 10¹⁵ (a thousand trillion). Commas and spaces are fine.

Try:

360 is not a prime number

It has 24 factors. The smallest prime that divides it is 2, so 360 = 2 × 180.

Prime factorisation

2³ × 3² × 5

= 2 × 2 × 2 × 3 × 3 × 5

Divide by primes, smallest first

Division ladder
Prime	Number
2	360
2	180
2	90
3	45
3	15
5	5
	1

How it’s calculated: divide by 2, 3, 5, 7 … while they go in. Large leftovers are tested with the Miller–Rabin prime test and split with Pollard’s rho method, so even 15-digit numbers take a moment.

Factors

How many factors: 24
Sum of all factors: 1,170

1
2
3
4
5
6
8
9
10
12
15
18
20
24
30
36
40
45
60
72
90
120
180
360

Factor pairs

1 × 360
2 × 180
3 × 120
4 × 90
5 × 72
6 × 60
8 × 45
9 × 40
10 × 36
12 × 30
15 × 24
18 × 20

Abundant: its factors other than itself add up to 810, which is more than 360.

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