What is the greatest common factor of 75 54 and 96?

Answer 1

One way to approach this is to look at the differences between the numbers. The difference between 54 and 75 is 21. The difference between 75 and 96 is 21. The greatest common factor cannot be larger than the smaller difference between the numbers and must be a factor of the difference. The factors of 21 are 1, 3, 7, and 21. The numbers are not divisible by 21, so try the next largest factor. The numbers are not divisible by 7, so try the next largest factor. The numbers are divisible by 3, so the greatest common factor is 3.

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

The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54.

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

The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

The common factors are 1 and 3. Therefore, the greatest common factor is 3.

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

The prime factors of 54 are 2, 3, 3, and 3.

The prime factors of 75 are 3, 5, and 5.

The prime factors of 96 are 2, 2, 2, 2, 2, and 3.

The prime factors in common are a single 3, so the greatest common factor is 3.

Answer 2

The greatest common factor (GCF) is: 3