What is the GCF of 36 and 78 showing work?

Answer 1

Write each of the numbers in their prime factorisation in power format; then the gcf is the product of the common primes to their lowest power:

36 = 22 x 32

78 = 2 x 3 x 13

gcf = 2 x 3 = 6

Alternatively:

Using Euclid's method:

Divide one number by the other to get a result (which is ignored) and a remainder;

Replace the first number by the second

Replace the second number (divisor) by the remainder

Repeat until the remainder is 0; then the GCF is the last divisor

36 ÷ 78 = [0] r 36

78 ÷ 36 = [2] r 6

36 ÷ 6 = [6] r 0

⇒ gcf = 6