What is the Greatest Common Factor of 75 and 89?

Greatest common factor (GCF) of 75 and 89 is 1.

GCF(75,89) = 1

We will now calculate the prime factors of 75 and 89, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75 and 89.

How to find the GCF of 75 and 89?

We will first find the prime factorization of 75 and 89. After we will calculate the factors of 75 and 89 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 89

Prime factors of 89 are 89. Prime factorization of 89 in exponential form is:

89 = 89¹

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 89

List of positive integer factors of 89 that divides 75 without a remainder.

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75 and 89. The biggest common factor number is the GCF number.
So the greatest common factor 75 and 89 is 1.

Also check out the Least Common Multiple of 75 and 89