What is the Greatest Common Factor of 75 and 60?

Greatest common factor (GCF) of 75 and 60 is 15.

GCF(75,60) = 15

We will now calculate the prime factors of 75 and 60, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75 and 60.

How to find the GCF of 75 and 60?

We will first find the prime factorization of 75 and 60. After we will calculate the factors of 75 and 60 and find the biggest common factor number .

Step-1: Prime Factorization of 75

Prime factors of 75 are 3, 5. Prime factorization of 75 in exponential form is:

75 = 3¹ × 5²

Step-2: Prime Factorization of 60

Prime factors of 60 are 2, 3, 5. Prime factorization of 60 in exponential form is:

60 = 2² × 3¹ × 5¹

Step-3: Factors of 75

List of positive integer factors of 75 that divides 75 without a remainder.

1, 3, 5, 15, 25

Step-4: Factors of 60

List of positive integer factors of 60 that divides 75 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75 and 60. The biggest common factor number is the GCF number.
So the greatest common factor 75 and 60 is 15.

Also check out the Least Common Multiple of 75 and 60