What is the Greatest Common Factor of 5300 and 5315?

Greatest common factor (GCF) of 5300 and 5315 is 5.

GCF(5300,5315) = 5

We will now calculate the prime factors of 5300 and 5315, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5300 and 5315.

How to find the GCF of 5300 and 5315?

We will first find the prime factorization of 5300 and 5315. After we will calculate the factors of 5300 and 5315 and find the biggest common factor number .

Step-1: Prime Factorization of 5300

Prime factors of 5300 are 2, 5, 53. Prime factorization of 5300 in exponential form is:

5300 = 2² × 5² × 53¹

Step-2: Prime Factorization of 5315

Prime factors of 5315 are 5, 1063. Prime factorization of 5315 in exponential form is:

5315 = 5¹ × 1063¹

Step-3: Factors of 5300

List of positive integer factors of 5300 that divides 5300 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 53, 100, 106, 212, 265, 530, 1060, 1325, 2650

Step-4: Factors of 5315

List of positive integer factors of 5315 that divides 5300 without a remainder.

1, 5, 1063

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5300 and 5315. The biggest common factor number is the GCF number.
So the greatest common factor 5300 and 5315 is 5.

Also check out the Least Common Multiple of 5300 and 5315