What are the methods to find the gcf of two numbers?

Answer 1

There are two main methods: prime factorisation and repeated differencing (Euclid's method).

Prime factorisation: this requires each number to be expressed as a product of their prime factors. The prime factorisations are compared to find common factors. The GCF is the product of these factors.

Euclid's method: this involves replacing the larger of the two numbers by the difference between the two numbers. Repeat with the new pair. You will either reach a point where the two numbers are the same - which is the GCF - or reach 1 in which case the numbers are coprime.

Answer 2

Example: 30 and 42

Factor them.

2 x 3 x 5 = 30

2 x 3 x 7 = 42

Select the common factors.

2 x 3 = 6, the GCF