What is the Greatest Common Factor of 75114 and 75128?

Greatest common factor (GCF) of 75114 and 75128 is 2.

GCF(75114,75128) = 2

We will now calculate the prime factors of 75114 and 75128, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75114 and 75128.

How to find the GCF of 75114 and 75128?

We will first find the prime factorization of 75114 and 75128. After we will calculate the factors of 75114 and 75128 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 75128

Prime factors of 75128 are 2, 9391. Prime factorization of 75128 in exponential form is:

75128 = 2³ × 9391¹

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 75128

List of positive integer factors of 75128 that divides 75114 without a remainder.

1, 2, 4, 8, 9391, 18782, 37564

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75114 and 75128. The biggest common factor number is the GCF number.
So the greatest common factor 75114 and 75128 is 2.

Also check out the Least Common Multiple of 75114 and 75128