What is the greatest common factor of 84 and 160?

Answer 1

Two methods come to mind:

A) Euclid's method

1. divide the first number by the second to get a quotient and remainder
2. if the remainder is not zero:
   1. replace the first number by the second number
   2. replace the second number by the remainder
   3. repeat from step 1
3. the gcf is the second number

for 84 and 66 this becomes:

84 ÷ 66 = 1 r 18

66 ÷ 18 = 3 r 12

18 ÷ 12 = 1 r 6

12 ÷ 6 = 2 r 0

→ gcf(84, 66) = 6.

B) Prime factorisation

Express each of the numbers in their prime factorisation in power format

The gcf is the product of the common primes to their lowest power.

For 84 and 66:

84 = 22 x 3 x 7

66 = 2 x 3 x 11

gcf = 2 x 3 = 6

Answer 2

The Greatest Common Factor (GCF) is: 2.

Answer 3

4