What is the Greatest Common Factor of 5109 and 5124?

Greatest common factor (GCF) of 5109 and 5124 is 3.

GCF(5109,5124) = 3

We will now calculate the prime factors of 5109 and 5124, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5109 and 5124.

How to find the GCF of 5109 and 5124?

We will first find the prime factorization of 5109 and 5124. After we will calculate the factors of 5109 and 5124 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 5124

Prime factors of 5124 are 2, 3, 7, 61. Prime factorization of 5124 in exponential form is:

5124 = 2² × 3¹ × 7¹ × 61¹

Step-3: Factors of 5109

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

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

Step-4: Factors of 5124

List of positive integer factors of 5124 that divides 5109 without a remainder.

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 61, 84, 122, 183, 244, 366, 427, 732, 854, 1281, 1708, 2562

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5109 and 5124. The biggest common factor number is the GCF number.
So the greatest common factor 5109 and 5124 is 3.

Also check out the Least Common Multiple of 5109 and 5124