What is the Greatest Common Factor of 8175 and 8184?

Greatest common factor (GCF) of 8175 and 8184 is 3.

GCF(8175,8184) = 3

We will now calculate the prime factors of 8175 and 8184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 8175 and 8184.

How to find the GCF of 8175 and 8184?

We will first find the prime factorization of 8175 and 8184. After we will calculate the factors of 8175 and 8184 and find the biggest common factor number .

Step-1: Prime Factorization of 8175

Prime factors of 8175 are 3, 5, 109. Prime factorization of 8175 in exponential form is:

8175 = 3¹ × 5² × 109¹

Step-2: Prime Factorization of 8184

Prime factors of 8184 are 2, 3, 11, 31. Prime factorization of 8184 in exponential form is:

8184 = 2³ × 3¹ × 11¹ × 31¹

Step-3: Factors of 8175

List of positive integer factors of 8175 that divides 8175 without a remainder.

1, 3, 5, 15, 25, 75, 109, 327, 545, 1635, 2725

Step-4: Factors of 8184

List of positive integer factors of 8184 that divides 8175 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 22, 24, 31, 33, 44, 62, 66, 88, 93, 124, 132, 186, 248, 264, 341, 372, 682, 744, 1023, 1364, 2046, 2728, 4092

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 8175 and 8184. The biggest common factor number is the GCF number.
So the greatest common factor 8175 and 8184 is 3.

Also check out the Least Common Multiple of 8175 and 8184