What is the Greatest Common Factor of 75312 and 75327?

Greatest common factor (GCF) of 75312 and 75327 is 3.

GCF(75312,75327) = 3

We will now calculate the prime factors of 75312 and 75327, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75312 and 75327.

How to find the GCF of 75312 and 75327?

We will first find the prime factorization of 75312 and 75327. After we will calculate the factors of 75312 and 75327 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 75327

Prime factors of 75327 are 3, 7, 17, 211. Prime factorization of 75327 in exponential form is:

75327 = 3¹ × 7¹ × 17¹ × 211¹

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 75327

List of positive integer factors of 75327 that divides 75312 without a remainder.

1, 3, 7, 17, 21, 51, 119, 211, 357, 633, 1477, 3587, 4431, 10761, 25109

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75312 and 75327. The biggest common factor number is the GCF number.
So the greatest common factor 75312 and 75327 is 3.

Also check out the Least Common Multiple of 75312 and 75327