What is the Greatest Common Factor of 5175 and 5190?

Greatest common factor (GCF) of 5175 and 5190 is 15.

GCF(5175,5190) = 15

We will now calculate the prime factors of 5175 and 5190, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5175 and 5190.

How to find the GCF of 5175 and 5190?

We will first find the prime factorization of 5175 and 5190. After we will calculate the factors of 5175 and 5190 and find the biggest common factor number .

Step-1: Prime Factorization of 5175

Prime factors of 5175 are 3, 5, 23. Prime factorization of 5175 in exponential form is:

5175 = 3² × 5² × 23¹

Step-2: Prime Factorization of 5190

Prime factors of 5190 are 2, 3, 5, 173. Prime factorization of 5190 in exponential form is:

5190 = 2¹ × 3¹ × 5¹ × 173¹

Step-3: Factors of 5175

List of positive integer factors of 5175 that divides 5175 without a remainder.

1, 3, 5, 9, 15, 23, 25, 45, 69, 75, 115, 207, 225, 345, 575, 1035, 1725

Step-4: Factors of 5190

List of positive integer factors of 5190 that divides 5175 without a remainder.

1, 2, 3, 5, 6, 10, 15, 30, 173, 346, 519, 865, 1038, 1730, 2595

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5175 and 5190. The biggest common factor number is the GCF number.
So the greatest common factor 5175 and 5190 is 15.

Also check out the Least Common Multiple of 5175 and 5190