What is the Greatest Common Factor of 75 and 87?

Greatest common factor (GCF) of 75 and 87 is 3.

GCF(75,87) = 3

We will now calculate the prime factors of 75 and 87, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75 and 87.

How to find the GCF of 75 and 87?

We will first find the prime factorization of 75 and 87. After we will calculate the factors of 75 and 87 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 87

Prime factors of 87 are 3, 29. Prime factorization of 87 in exponential form is:

87 = 3¹ × 29¹

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 87

List of positive integer factors of 87 that divides 75 without a remainder.

1, 3, 29

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75 and 87. The biggest common factor number is the GCF number.
So the greatest common factor 75 and 87 is 3.

Also check out the Least Common Multiple of 75 and 87