What is the Greatest Common Factor of 75216 and 75228?

Greatest common factor (GCF) of 75216 and 75228 is 12.

GCF(75216,75228) = 12

We will now calculate the prime factors of 75216 and 75228, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75216 and 75228.

How to find the GCF of 75216 and 75228?

We will first find the prime factorization of 75216 and 75228. After we will calculate the factors of 75216 and 75228 and find the biggest common factor number .

Step-1: Prime Factorization of 75216

Prime factors of 75216 are 2, 3, 1567. Prime factorization of 75216 in exponential form is:

75216 = 2⁴ × 3¹ × 1567¹

Step-2: Prime Factorization of 75228

Prime factors of 75228 are 2, 3, 6269. Prime factorization of 75228 in exponential form is:

75228 = 2² × 3¹ × 6269¹

Step-3: Factors of 75216

List of positive integer factors of 75216 that divides 75216 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 1567, 3134, 4701, 6268, 9402, 12536, 18804, 25072, 37608

Step-4: Factors of 75228

List of positive integer factors of 75228 that divides 75216 without a remainder.

1, 2, 3, 4, 6, 12, 6269, 12538, 18807, 25076, 37614

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75216 and 75228. The biggest common factor number is the GCF number.
So the greatest common factor 75216 and 75228 is 12.

Also check out the Least Common Multiple of 75216 and 75228