What is the Greatest Common Factor of 75 and 90?

Greatest common factor (GCF) of 75 and 90 is 15.

GCF(75,90) = 15

We will now calculate the prime factors of 75 and 90, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75 and 90.

How to find the GCF of 75 and 90?

We will first find the prime factorization of 75 and 90. After we will calculate the factors of 75 and 90 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 90

Prime factors of 90 are 2, 3, 5. Prime factorization of 90 in exponential form is:

90 = 2¹ × 3² × 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 90

List of positive integer factors of 90 that divides 75 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75 and 90. The biggest common factor number is the GCF number.
So the greatest common factor 75 and 90 is 15.

Also check out the Least Common Multiple of 75 and 90