What is the Greatest Common Factor of 342 and 361?

Greatest common factor (GCF) of 342 and 361 is 19.

GCF(342,361) = 19

We will now calculate the prime factors of 342 and 361, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 342 and 361.

How to find the GCF of 342 and 361?

We will first find the prime factorization of 342 and 361. After we will calculate the factors of 342 and 361 and find the biggest common factor number .

Step-1: Prime Factorization of 342

Prime factors of 342 are 2, 3, 19. Prime factorization of 342 in exponential form is:

342 = 2¹ × 3² × 19¹

Step-2: Prime Factorization of 361

Prime factors of 361 are 19. Prime factorization of 361 in exponential form is:

361 = 19²

Step-3: Factors of 342

List of positive integer factors of 342 that divides 342 without a remainder.

1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171

Step-4: Factors of 361

List of positive integer factors of 361 that divides 342 without a remainder.

1, 19

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 342 and 361. The biggest common factor number is the GCF number.
So the greatest common factor 342 and 361 is 19.

Also check out the Least Common Multiple of 342 and 361