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Find the greatest common factor of 735 and 1050

How to find the greatest common factor of 735 and 1050?

Find the gcf of 735 and 1050

Problem. Find the greatest common factor of 735 and 1050.

Solution.

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

The prime factorization of 735

735 =
3 * 5 * 7 * 7

See 735 prime factorization.

The prime factorization of 1050

1050 =
2 * 3 * 5 * 5 * 7

See 1050 prime factorization.

Find the common prime factors of these two numbers 735 and 1050

735 –> (3, 5, 7, 7)
1050 –> (2, 3, 5, 5, 7)

The common factors of 735 and 1050 are

3, 5, 7

The product of these common prime factors is the greatest common factor of 735 and 1050

3 * 5 * 7 = 105

The gcf of 735 and 1050 is 105

gcf(735, 1050) = 105

The problem is solved.