What is the Greatest Common Factor of 6375 and 6384?

Greatest common factor (GCF) of 6375 and 6384 is 3.

GCF(6375,6384) = 3

We will now calculate the prime factors of 6375 and 6384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 6375 and 6384.

How to find the GCF of 6375 and 6384?

We will first find the prime factorization of 6375 and 6384. After we will calculate the factors of 6375 and 6384 and find the biggest common factor number .

Step-1: Prime Factorization of 6375

Prime factors of 6375 are 3, 5, 17. Prime factorization of 6375 in exponential form is:

6375 = 3¹ × 5³ × 17¹

Step-2: Prime Factorization of 6384

Prime factors of 6384 are 2, 3, 7, 19. Prime factorization of 6384 in exponential form is:

6384 = 2⁴ × 3¹ × 7¹ × 19¹

Step-3: Factors of 6375

List of positive integer factors of 6375 that divides 6375 without a remainder.

1, 3, 5, 15, 17, 25, 51, 75, 85, 125, 255, 375, 425, 1275, 2125

Step-4: Factors of 6384

List of positive integer factors of 6384 that divides 6375 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 19, 21, 24, 28, 38, 42, 48, 56, 57, 76, 84, 112, 114, 133, 152, 168, 228, 266, 304, 336, 399, 456, 532, 798, 912, 1064, 1596, 2128, 3192

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 6375 and 6384. The biggest common factor number is the GCF number.
So the greatest common factor 6375 and 6384 is 3.

Also check out the Least Common Multiple of 6375 and 6384