What is the Greatest Common Factor of 364 and 378?

Greatest common factor (GCF) of 364 and 378 is 14.

GCF(364,378) = 14

We will now calculate the prime factors of 364 and 378, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 364 and 378.

How to find the GCF of 364 and 378?

We will first find the prime factorization of 364 and 378. After we will calculate the factors of 364 and 378 and find the biggest common factor number .

Step-1: Prime Factorization of 364

Prime factors of 364 are 2, 7, 13. Prime factorization of 364 in exponential form is:

364 = 2² × 7¹ × 13¹

Step-2: 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-3: Factors of 364

List of positive integer factors of 364 that divides 364 without a remainder.

1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182

Step-4: Factors of 378

List of positive integer factors of 378 that divides 364 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 364 and 378. The biggest common factor number is the GCF number.
So the greatest common factor 364 and 378 is 14.

Also check out the Least Common Multiple of 364 and 378