What is the greatest common factor of 45 and 50?

Answer 1

One way to approach this is to look at the difference between 45 and 50, which is 5. The greatest common factor of two numbers cannot be larger than the difference between the two numbers and must be a factor of the difference. Since both 45 and 50 are divisible by 5, the greatest common factor is 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 50 are 1, 2, 5, 10, 25, and 50.

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 50 are 2, 5, and 5.

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