What is the Greatest Common Factor of 375 and 390?

Greatest common factor (GCF) of 375 and 390 is 15.

GCF(375,390) = 15

We will now calculate the prime factors of 375 and 390, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 375 and 390.

How to find the GCF of 375 and 390?

We will first find the prime factorization of 375 and 390. After we will calculate the factors of 375 and 390 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 390

Prime factors of 390 are 2, 3, 5, 13. Prime factorization of 390 in exponential form is:

390 = 2¹ × 3¹ × 5¹ × 13¹

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 390

List of positive integer factors of 390 that divides 375 without a remainder.

1, 2, 3, 5, 6, 10, 13, 15, 26, 30, 39, 65, 78, 130, 195

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 375 and 390. The biggest common factor number is the GCF number.
So the greatest common factor 375 and 390 is 15.

Also check out the Least Common Multiple of 375 and 390