What is the Greatest Common Factor of 378 and 385?

Greatest common factor (GCF) of 378 and 385 is 7.

GCF(378,385) = 7

We will now calculate the prime factors of 378 and 385, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 378 and 385.

How to find the GCF of 378 and 385?

We will first find the prime factorization of 378 and 385. After we will calculate the factors of 378 and 385 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 385

Prime factors of 385 are 5, 7, 11. Prime factorization of 385 in exponential form is:

385 = 5¹ × 7¹ × 11¹

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 385

List of positive integer factors of 385 that divides 378 without a remainder.

1, 5, 7, 11, 35, 55, 77

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 378 and 385. The biggest common factor number is the GCF number.
So the greatest common factor 378 and 385 is 7.

Also check out the Least Common Multiple of 378 and 385