What is the Greatest Common Factor of 75114 and 75132?

Greatest common factor (GCF) of 75114 and 75132 is 18.

GCF(75114,75132) = 18

We will now calculate the prime factors of 75114 and 75132, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75114 and 75132.

How to find the GCF of 75114 and 75132?

We will first find the prime factorization of 75114 and 75132. After we will calculate the factors of 75114 and 75132 and find the biggest common factor number .

Step-1: Prime Factorization of 75114

Prime factors of 75114 are 2, 3, 13, 107. Prime factorization of 75114 in exponential form is:

75114 = 2¹ × 3³ × 13¹ × 107¹

Step-2: 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-3: Factors of 75114

List of positive integer factors of 75114 that divides 75114 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 107, 117, 214, 234, 321, 351, 642, 702, 963, 1391, 1926, 2782, 2889, 4173, 5778, 8346, 12519, 25038, 37557

Step-4: Factors of 75132

List of positive integer factors of 75132 that divides 75114 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75114 and 75132. The biggest common factor number is the GCF number.
So the greatest common factor 75114 and 75132 is 18.

Also check out the Least Common Multiple of 75114 and 75132