What is the Greatest Common Factor of 369 and 380?

Greatest common factor (GCF) of 369 and 380 is 1.

GCF(369,380) = 1

We will now calculate the prime factors of 369 and 380, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 369 and 380.

How to find the GCF of 369 and 380?

We will first find the prime factorization of 369 and 380. After we will calculate the factors of 369 and 380 and find the biggest common factor number .

Step-1: Prime Factorization of 369

Prime factors of 369 are 3, 41. Prime factorization of 369 in exponential form is:

369 = 3² × 41¹

Step-2: Prime Factorization of 380

Prime factors of 380 are 2, 5, 19. Prime factorization of 380 in exponential form is:

380 = 2² × 5¹ × 19¹

Step-3: Factors of 369

List of positive integer factors of 369 that divides 369 without a remainder.

1, 3, 9, 41, 123

Step-4: Factors of 380

List of positive integer factors of 380 that divides 369 without a remainder.

1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 369 and 380. The biggest common factor number is the GCF number.
So the greatest common factor 369 and 380 is 1.

Also check out the Least Common Multiple of 369 and 380