What is the greatest common factor of 525 and 1000?

Answer 1

One way to determine the greatest common factor is to find all the factors of the numbers and compare them.

The factors of 525 are 1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 175 and 525.

The factors of 1000 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.

The common factors are 1, 5, and 25. Therefore, the greatest common factor is 25.

The greatest common factor can also be calculated by identifying the common prime factors and multiplying them together.

The prime factors of 525 are 3, 5, 5, and 7.

The prime factors of 1000 are 2, 2, 2, 5, 5, and 5.

The prime factors in common are 5 and 5, so the greatest common factor is 5 x 5 = 25.

Another way to approach this would be to make a reasonable guess. Any number that ends in 25, 50, 75, or 00 is divisible by 25. So divide both numbers by 25 and compare the results.

525 ÷ 25 = 21

1000 ÷ 25 = 40

Since 21 (which is 3 x 7) and 40 (which is 2 x 2 x 2 x 5) have no factors in common, the greatest common factor is 25.