What is the Greatest Common Factor of 378 and 390?

Greatest common factor (GCF) of 378 and 390 is 6.

GCF(378,390) = 6

We will now calculate the prime factors of 378 and 390, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 378 and 390.

How to find the GCF of 378 and 390?

We will first find the prime factorization of 378 and 390. After we will calculate the factors of 378 and 390 and find the biggest common factor number .

Step-1: Prime Factorization of 378

Prime factors of 378 are 2, 3, 7. Prime factorization of 378 in exponential form is:

378 = 2¹ × 3³ × 7¹

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 378

List of positive integer factors of 378 that divides 378 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189

Step-4: Factors of 390

List of positive integer factors of 390 that divides 378 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 378 and 390. The biggest common factor number is the GCF number.
So the greatest common factor 378 and 390 is 6.

Also check out the Least Common Multiple of 378 and 390