What is the Greatest Common Factor of 375 and 384?

Greatest common factor (GCF) of 375 and 384 is 3.

GCF(375,384) = 3

We will now calculate the prime factors of 375 and 384, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 375 and 384.

How to find the GCF of 375 and 384?

We will first find the prime factorization of 375 and 384. After we will calculate the factors of 375 and 384 and find the biggest common factor number .

Step-1: Prime Factorization of 375

Prime factors of 375 are 3, 5. Prime factorization of 375 in exponential form is:

375 = 3¹ × 5³

Step-2: Prime Factorization of 384

Prime factors of 384 are 2, 3. Prime factorization of 384 in exponential form is:

384 = 2⁷ × 3¹

Step-3: Factors of 375

List of positive integer factors of 375 that divides 375 without a remainder.

1, 3, 5, 15, 25, 75, 125

Step-4: Factors of 384

List of positive integer factors of 384 that divides 375 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 375 and 384. The biggest common factor number is the GCF number.
So the greatest common factor 375 and 384 is 3.

Also check out the Least Common Multiple of 375 and 384