What is the Greatest Common Factor of 75114 and 75123?

Greatest common factor (GCF) of 75114 and 75123 is 9.

GCF(75114,75123) = 9

We will now calculate the prime factors of 75114 and 75123, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75114 and 75123.

How to find the GCF of 75114 and 75123?

We will first find the prime factorization of 75114 and 75123. After we will calculate the factors of 75114 and 75123 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 75123

Prime factors of 75123 are 3, 17, 491. Prime factorization of 75123 in exponential form is:

75123 = 3² × 17¹ × 491¹

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 75123

List of positive integer factors of 75123 that divides 75114 without a remainder.

1, 3, 9, 17, 51, 153, 491, 1473, 4419, 8347, 25041

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75114 and 75123. The biggest common factor number is the GCF number.
So the greatest common factor 75114 and 75123 is 9.

Also check out the Least Common Multiple of 75114 and 75123