What is the Greatest Common Factor of 369 and 375?

Greatest common factor (GCF) of 369 and 375 is 3.

GCF(369,375) = 3

We will now calculate the prime factors of 369 and 375, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 369 and 375.

How to find the GCF of 369 and 375?

We will first find the prime factorization of 369 and 375. After we will calculate the factors of 369 and 375 and find the biggest common factor number .

Step-1: Prime Factorization of 369

Prime factors of 369 are 3, 41. Prime factorization of 369 in exponential form is:

369 = 3² × 41¹

Step-2: Prime Factorization of 375

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

375 = 3¹ × 5³

Step-3: Factors of 369

List of positive integer factors of 369 that divides 369 without a remainder.

1, 3, 9, 41, 123

Step-4: Factors of 375

List of positive integer factors of 375 that divides 369 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 369 and 375. The biggest common factor number is the GCF number.
So the greatest common factor 369 and 375 is 3.

Also check out the Least Common Multiple of 369 and 375