What is the Greatest Common Factor of 365 and 369?

Greatest common factor (GCF) of 365 and 369 is 1.

GCF(365,369) = 1

We will now calculate the prime factors of 365 and 369, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 365 and 369.

How to find the GCF of 365 and 369?

We will first find the prime factorization of 365 and 369. After we will calculate the factors of 365 and 369 and find the biggest common factor number .

Step-1: Prime Factorization of 365

Prime factors of 365 are 5, 73. Prime factorization of 365 in exponential form is:

365 = 5¹ × 73¹

Step-2: Prime Factorization of 369

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

369 = 3² × 41¹

Step-3: Factors of 365

List of positive integer factors of 365 that divides 365 without a remainder.

1, 5, 73

Step-4: Factors of 369

List of positive integer factors of 369 that divides 365 without a remainder.

1, 3, 9, 41, 123

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 365 and 369. The biggest common factor number is the GCF number.
So the greatest common factor 365 and 369 is 1.

Also check out the Least Common Multiple of 365 and 369