What is the Greatest Common Factor of 75132 and 75144?

Greatest common factor (GCF) of 75132 and 75144 is 12.

GCF(75132,75144) = 12

We will now calculate the prime factors of 75132 and 75144, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75132 and 75144.

How to find the GCF of 75132 and 75144?

We will first find the prime factorization of 75132 and 75144. After we will calculate the factors of 75132 and 75144 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 75144

Prime factors of 75144 are 2, 3, 31, 101. Prime factorization of 75144 in exponential form is:

75144 = 2³ × 3¹ × 31¹ × 101¹

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 75144

List of positive integer factors of 75144 that divides 75132 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 31, 62, 93, 101, 124, 186, 202, 248, 303, 372, 404, 606, 744, 808, 1212, 2424, 3131, 6262, 9393, 12524, 18786, 25048, 37572

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75132 and 75144. The biggest common factor number is the GCF number.
So the greatest common factor 75132 and 75144 is 12.

Also check out the Least Common Multiple of 75132 and 75144