What is the Greatest Common Factor of 5100 and 5114?

Greatest common factor (GCF) of 5100 and 5114 is 2.

GCF(5100,5114) = 2

We will now calculate the prime factors of 5100 and 5114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5100 and 5114.

How to find the GCF of 5100 and 5114?

We will first find the prime factorization of 5100 and 5114. After we will calculate the factors of 5100 and 5114 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 5114

Prime factors of 5114 are 2, 2557. Prime factorization of 5114 in exponential form is:

5114 = 2¹ × 2557¹

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 5114

List of positive integer factors of 5114 that divides 5100 without a remainder.

1, 2, 2557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5100 and 5114. The biggest common factor number is the GCF number.
So the greatest common factor 5100 and 5114 is 2.

Also check out the Least Common Multiple of 5100 and 5114