What is the Greatest Common Factor of 5088 and 5100?

Greatest common factor (GCF) of 5088 and 5100 is 12.

GCF(5088,5100) = 12

We will now calculate the prime factors of 5088 and 5100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5088 and 5100.

How to find the GCF of 5088 and 5100?

We will first find the prime factorization of 5088 and 5100. After we will calculate the factors of 5088 and 5100 and find the biggest common factor number .

Step-1: Prime Factorization of 5088

Prime factors of 5088 are 2, 3, 53. Prime factorization of 5088 in exponential form is:

5088 = 2⁵ × 3¹ × 53¹

Step-2: Prime Factorization of 5100

Prime factors of 5100 are 2, 3, 5, 17. Prime factorization of 5100 in exponential form is:

5100 = 2² × 3¹ × 5² × 17¹

Step-3: Factors of 5088

List of positive integer factors of 5088 that divides 5088 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 53, 96, 106, 159, 212, 318, 424, 636, 848, 1272, 1696, 2544

Step-4: Factors of 5100

List of positive integer factors of 5100 that divides 5088 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 17, 20, 25, 30, 34, 50, 51, 60, 68, 75, 85, 100, 102, 150, 170, 204, 255, 300, 340, 425, 510, 850, 1020, 1275, 1700, 2550

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5088 and 5100. The biggest common factor number is the GCF number.
So the greatest common factor 5088 and 5100 is 12.

Also check out the Least Common Multiple of 5088 and 5100