What is the greatest common factor of 125 150 and 225?

Answer 1

The GCF of 125, 150, and 225 is 25.

One way to approach this is to look at the difference between the numbers. The greatest common factor of two or more numbers cannot be larger than the smallest difference between two of the numbers and must be a factor of the difference. The difference between 125 and 150 is 25. The difference between 150 and 225 is 75. So, the greatest common factor must be a factor of 25. Since 125, 150, and 225 are all divisible by 25, the greatest common factor is 25.

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

The factors of 125 are 1, 5, 25, and 125.

The factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, and 150.

The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, and 225.

The common factors are 1, 3, 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 125 are 5, 5, and 5.

The prime factors of 150 are 2, 3, 5, and 5.

The prime factors of 225 are 3, 3, 5, and 5.

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