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Find the greatest common factor of 180 and 450

How to find the greatest common factor of 180 and 450?

Find the gcf of 180 and 450

Problem. Find the greatest common factor of 180 and 450.

Solution.

See How to find the greatest common factor of two numbers?

The prime factorization of 180

180 =
2 * 2 * 3 * 3 * 5

See 180 prime factorization.

The prime factorization of 450

450 =
2 * 3 * 3 * 5 * 5

See 450 prime factorization.

Find the common prime factors of these two numbers 180 and 450

180 –> (2, 2, 3, 3, 5)
450 –> (2, 3, 3, 5, 5)

The common factors of 180 and 450 are

2, 3, 3, 5

The product of these common prime factors is the greatest common factor of 180 and 450

2 * 3 * 3 * 5 = 90

The gcf of 180 and 450 is 90

gcf(180, 450) = 90

The problem is solved.