What is the gcf of 200 and 250 and 400?

Answer 1

We firstly have to express each of these numbers as a product of their prime factors.

200 = 23x52

250 = 2 x53

400 = 24x52

We now collect all the prime factor indices that are common to ALL of the numbers.

HCF - 2 x 52 = 50

Answer 2

The factors of 200 are:

1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 200

The factors of 250 are:

1, 2, 5, 10, 25, 50, 125, 250

The factors of 400 are:

1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400

The common factors are:

1, 2, 5, 10, 25, 50

The Greatest Common Factor (GCF) is:

50