What is the Greatest Common Factor of 363 and 378?

Greatest common factor (GCF) of 363 and 378 is 3.

GCF(363,378) = 3

We will now calculate the prime factors of 363 and 378, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 363 and 378.

How to find the GCF of 363 and 378?

We will first find the prime factorization of 363 and 378. After we will calculate the factors of 363 and 378 and find the biggest common factor number .

Step-1: Prime Factorization of 363

Prime factors of 363 are 3, 11. Prime factorization of 363 in exponential form is:

363 = 3¹ × 11²

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 363

List of positive integer factors of 363 that divides 363 without a remainder.

1, 3, 11, 33, 121

Step-4: Factors of 378

List of positive integer factors of 378 that divides 363 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 363 and 378. The biggest common factor number is the GCF number.
So the greatest common factor 363 and 378 is 3.

Also check out the Least Common Multiple of 363 and 378