What is the Greatest Common Factor of 75072 and 75084?

Greatest common factor (GCF) of 75072 and 75084 is 12.

GCF(75072,75084) = 12

We will now calculate the prime factors of 75072 and 75084, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75072 and 75084.

How to find the GCF of 75072 and 75084?

We will first find the prime factorization of 75072 and 75084. After we will calculate the factors of 75072 and 75084 and find the biggest common factor number .

Step-1: Prime Factorization of 75072

Prime factors of 75072 are 2, 3, 17, 23. Prime factorization of 75072 in exponential form is:

75072 = 2⁶ × 3¹ × 17¹ × 23¹

Step-2: Prime Factorization of 75084

Prime factors of 75084 are 2, 3, 6257. Prime factorization of 75084 in exponential form is:

75084 = 2² × 3¹ × 6257¹

Step-3: Factors of 75072

List of positive integer factors of 75072 that divides 75072 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 17, 23, 24, 32, 34, 46, 48, 51, 64, 68, 69, 92, 96, 102, 136, 138, 184, 192, 204, 272, 276, 368, 391, 408, 544, 552, 736, 782, 816, 1088, 1104, 1173, 1472, 1564, 1632, 2208, 2346, 3128, 3264, 4416, 4692, 6256, 9384, 12512, 18768, 25024, 37536

Step-4: Factors of 75084

List of positive integer factors of 75084 that divides 75072 without a remainder.

1, 2, 3, 4, 6, 12, 6257, 12514, 18771, 25028, 37542

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75072 and 75084. The biggest common factor number is the GCF number.
So the greatest common factor 75072 and 75084 is 12.

Also check out the Least Common Multiple of 75072 and 75084