What is the Greatest Common Factor of 5085 and 5100?

Greatest common factor (GCF) of 5085 and 5100 is 15.

GCF(5085,5100) = 15

We will now calculate the prime factors of 5085 and 5100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5085 and 5100.

How to find the GCF of 5085 and 5100?

We will first find the prime factorization of 5085 and 5100. After we will calculate the factors of 5085 and 5100 and find the biggest common factor number .

Step-1: Prime Factorization of 5085

Prime factors of 5085 are 3, 5, 113. Prime factorization of 5085 in exponential form is:

5085 = 3² × 5¹ × 113¹

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 5085

List of positive integer factors of 5085 that divides 5085 without a remainder.

1, 3, 5, 9, 15, 45, 113, 339, 565, 1017, 1695

Step-4: Factors of 5100

List of positive integer factors of 5100 that divides 5085 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 5085 and 5100. The biggest common factor number is the GCF number.
So the greatest common factor 5085 and 5100 is 15.

Also check out the Least Common Multiple of 5085 and 5100