What is the Greatest Common Factor of 378 and 392?

Greatest common factor (GCF) of 378 and 392 is 14.

GCF(378,392) = 14

We will now calculate the prime factors of 378 and 392, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 378 and 392.

How to find the GCF of 378 and 392?

We will first find the prime factorization of 378 and 392. After we will calculate the factors of 378 and 392 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 392

Prime factors of 392 are 2, 7. Prime factorization of 392 in exponential form is:

392 = 2³ × 7²

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 392

List of positive integer factors of 392 that divides 378 without a remainder.

1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 378 and 392. The biggest common factor number is the GCF number.
So the greatest common factor 378 and 392 is 14.

Also check out the Least Common Multiple of 378 and 392