What is the Greatest Common Factor of 75084 and 75096?

Greatest common factor (GCF) of 75084 and 75096 is 12.

GCF(75084,75096) = 12

We will now calculate the prime factors of 75084 and 75096, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75084 and 75096.

How to find the GCF of 75084 and 75096?

We will first find the prime factorization of 75084 and 75096. After we will calculate the factors of 75084 and 75096 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 75096

Prime factors of 75096 are 2, 3, 7, 149. Prime factorization of 75096 in exponential form is:

75096 = 2³ × 3² × 7¹ × 149¹

Step-3: Factors of 75084

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

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

Step-4: Factors of 75096

List of positive integer factors of 75096 that divides 75084 without a remainder.

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 28, 36, 42, 56, 63, 72, 84, 126, 149, 168, 252, 298, 447, 504, 596, 894, 1043, 1192, 1341, 1788, 2086, 2682, 3129, 3576, 4172, 5364, 6258, 8344, 9387, 10728, 12516, 18774, 25032, 37548

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75084 and 75096. The biggest common factor number is the GCF number.
So the greatest common factor 75084 and 75096 is 12.

Also check out the Least Common Multiple of 75084 and 75096