What is the Greatest Common Factor of 378 and 398?

Greatest common factor (GCF) of 378 and 398 is 2.

GCF(378,398) = 2

We will now calculate the prime factors of 378 and 398, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 378 and 398.

How to find the GCF of 378 and 398?

We will first find the prime factorization of 378 and 398. After we will calculate the factors of 378 and 398 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 398

Prime factors of 398 are 2, 199. Prime factorization of 398 in exponential form is:

398 = 2¹ × 199¹

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 398

List of positive integer factors of 398 that divides 378 without a remainder.

1, 2, 199

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 378 and 398. The biggest common factor number is the GCF number.
So the greatest common factor 378 and 398 is 2.

Also check out the Least Common Multiple of 378 and 398