What is the Greatest Common Factor of 5175 and 5184?

Greatest common factor (GCF) of 5175 and 5184 is 9.

GCF(5175,5184) = 9

We will now calculate the prime factors of 5175 and 5184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 5175 and 5184.

How to find the GCF of 5175 and 5184?

We will first find the prime factorization of 5175 and 5184. After we will calculate the factors of 5175 and 5184 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 5184

Prime factors of 5184 are 2, 3. Prime factorization of 5184 in exponential form is:

5184 = 2⁶ × 3⁴

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 5184

List of positive integer factors of 5184 that divides 5175 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 5175 and 5184. The biggest common factor number is the GCF number.
So the greatest common factor 5175 and 5184 is 9.

Also check out the Least Common Multiple of 5175 and 5184