What is the Greatest Common Factor of 75288 and 75300?

Greatest common factor (GCF) of 75288 and 75300 is 12.

GCF(75288,75300) = 12

We will now calculate the prime factors of 75288 and 75300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 75288 and 75300.

How to find the GCF of 75288 and 75300?

We will first find the prime factorization of 75288 and 75300. After we will calculate the factors of 75288 and 75300 and find the biggest common factor number .

Step-1: Prime Factorization of 75288

Prime factors of 75288 are 2, 3, 3137. Prime factorization of 75288 in exponential form is:

75288 = 2³ × 3¹ × 3137¹

Step-2: Prime Factorization of 75300

Prime factors of 75300 are 2, 3, 5, 251. Prime factorization of 75300 in exponential form is:

75300 = 2² × 3¹ × 5² × 251¹

Step-3: Factors of 75288

List of positive integer factors of 75288 that divides 75288 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 3137, 6274, 9411, 12548, 18822, 25096, 37644

Step-4: Factors of 75300

List of positive integer factors of 75300 that divides 75288 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 251, 300, 502, 753, 1004, 1255, 1506, 2510, 3012, 3765, 5020, 6275, 7530, 12550, 15060, 18825, 25100, 37650

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 75288 and 75300. The biggest common factor number is the GCF number.
So the greatest common factor 75288 and 75300 is 12.

Also check out the Least Common Multiple of 75288 and 75300