How do you find the greatest common factor of 18 and 20?

Answer 1

Various methods:

• Express both the numbers as their prime factorisations in power format. The gcf is the product of the lowest powers of the common primes:

18 = 2 x 32

20 = 22 x 5

Common prime(s): 2

Lowest power is in 18 where it is 21 (=2)

So gcf = 2.

• Euclid's method:

1. Find the remainder of dividing the first number by the second
2. if the remainder is zero, the gcf is the second number.
3. Repeat from step 1 with the second number as the first number and the remainder as the second number.

So for 18 & 20:

18 ÷ 20 = [0] remainder 18

20 ÷ 18 = [1] remainder 2

18 ÷ 2 = [9] remainder 0

So gcf is 2.