What is the greatest common factor of 45 and 250?

Answer 1

Since the numbers end in either 5 or 0, you know that they are both divisible by, which means the greatest common factor is a multiple of 5. If you divide both numbers by 5, you get 45 ÷ 5 = 9 and 250 ÷ 5 = 50. The results, 9 and 50, do not have any factors in common, since the only factors of 9 besides 1 are multiples of 3, and 50 is not divisible by 3. Therefore, the greatest common factor must be 5.

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

The factors of 45 are 1, 3, 5, 9, 15, and 45.

The factors of 250 are 1, 2, 5, 10, 25, 50, 125, and 250.

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

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

The prime factors of 45 are 3, 3, and 5.

The prime factors of 250 are 2, 5, 5, and 5.

The prime factors in common are a single 5, so the greatest common factor is 5.