What is the Greatest Common Factor of 75132 and 75138?

Greatest common factor (GCF) of 75132 and 75138 is 6.

GCF(75132,75138) = 6

We will now calculate the prime factors of 75132 and 75138, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75132 and 75138.

How to find the GCF of 75132 and 75138?

We will first find the prime factorization of 75132 and 75138. After we will calculate the factors of 75132 and 75138 and find the biggest common factor number .

Step-1: Prime Factorization of 75132

Prime factors of 75132 are 2, 3, 2087. Prime factorization of 75132 in exponential form is:

75132 = 2² × 3² × 2087¹

Step-2: Prime Factorization of 75138

Prime factors of 75138 are 2, 3, 7, 1789. Prime factorization of 75138 in exponential form is:

75138 = 2¹ × 3¹ × 7¹ × 1789¹

Step-3: Factors of 75132

List of positive integer factors of 75132 that divides 75132 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 2087, 4174, 6261, 8348, 12522, 18783, 25044, 37566

Step-4: Factors of 75138

List of positive integer factors of 75138 that divides 75132 without a remainder.

1, 2, 3, 6, 7, 14, 21, 42, 1789, 3578, 5367, 10734, 12523, 25046, 37569

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75132 and 75138. The biggest common factor number is the GCF number.
So the greatest common factor 75132 and 75138 is 6.

Also check out the Least Common Multiple of 75132 and 75138