What is the Greatest Common Factor of 364 and 382?

Greatest common factor (GCF) of 364 and 382 is 2.

GCF(364,382) = 2

We will now calculate the prime factors of 364 and 382, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 364 and 382.

How to find the GCF of 364 and 382?

We will first find the prime factorization of 364 and 382. After we will calculate the factors of 364 and 382 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 382

Prime factors of 382 are 2, 191. Prime factorization of 382 in exponential form is:

382 = 2¹ × 191¹

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 382

List of positive integer factors of 382 that divides 364 without a remainder.

1, 2, 191

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 364 and 382. The biggest common factor number is the GCF number.
So the greatest common factor 364 and 382 is 2.

Also check out the Least Common Multiple of 364 and 382