What is the Greatest Common Factor of 5100 and 5109?

Greatest common factor (GCF) of 5100 and 5109 is 3.

GCF(5100,5109) = 3

We will now calculate the prime factors of 5100 and 5109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5100 and 5109.

How to find the GCF of 5100 and 5109?

We will first find the prime factorization of 5100 and 5109. After we will calculate the factors of 5100 and 5109 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 5109

Prime factors of 5109 are 3, 13, 131. Prime factorization of 5109 in exponential form is:

5109 = 3¹ × 13¹ × 131¹

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 5109

List of positive integer factors of 5109 that divides 5100 without a remainder.

1, 3, 13, 39, 131, 393, 1703

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5100 and 5109. The biggest common factor number is the GCF number.
So the greatest common factor 5100 and 5109 is 3.

Also check out the Least Common Multiple of 5100 and 5109