What is the Greatest Common Factor of 75312 and 75330?

Greatest common factor (GCF) of 75312 and 75330 is 18.

GCF(75312,75330) = 18

We will now calculate the prime factors of 75312 and 75330, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75312 and 75330.

How to find the GCF of 75312 and 75330?

We will first find the prime factorization of 75312 and 75330. After we will calculate the factors of 75312 and 75330 and find the biggest common factor number .

Step-1: Prime Factorization of 75312

Prime factors of 75312 are 2, 3, 523. Prime factorization of 75312 in exponential form is:

75312 = 2⁴ × 3² × 523¹

Step-2: Prime Factorization of 75330

Prime factors of 75330 are 2, 3, 5, 31. Prime factorization of 75330 in exponential form is:

75330 = 2¹ × 3⁵ × 5¹ × 31¹

Step-3: Factors of 75312

List of positive integer factors of 75312 that divides 75312 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 523, 1046, 1569, 2092, 3138, 4184, 4707, 6276, 8368, 9414, 12552, 18828, 25104, 37656

Step-4: Factors of 75330

List of positive integer factors of 75330 that divides 75312 without a remainder.

1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 31, 45, 54, 62, 81, 90, 93, 135, 155, 162, 186, 243, 270, 279, 310, 405, 465, 486, 558, 810, 837, 930, 1215, 1395, 1674, 2430, 2511, 2790, 4185, 5022, 7533, 8370, 12555, 15066, 25110, 37665

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75312 and 75330. The biggest common factor number is the GCF number.
So the greatest common factor 75312 and 75330 is 18.

Also check out the Least Common Multiple of 75312 and 75330