What is the Greatest Common Factor of 5100 and 5112?

Greatest common factor (GCF) of 5100 and 5112 is 12.

GCF(5100,5112) = 12

We will now calculate the prime factors of 5100 and 5112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5100 and 5112.

How to find the GCF of 5100 and 5112?

We will first find the prime factorization of 5100 and 5112. After we will calculate the factors of 5100 and 5112 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5112

Prime factors of 5112 are 2, 3, 71. Prime factorization of 5112 in exponential form is:

5112 = 2³ × 3² × 71¹

Step-3: Factors of 5100

List of positive integer factors of 5100 that divides 5100 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

Step-4: Factors of 5112

List of positive integer factors of 5112 that divides 5100 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 71, 72, 142, 213, 284, 426, 568, 639, 852, 1278, 1704, 2556

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5100 and 5112. The biggest common factor number is the GCF number.
So the greatest common factor 5100 and 5112 is 12.

Also check out the Least Common Multiple of 5100 and 5112