What is the Greatest Common Factor of 365 and 370?

Greatest common factor (GCF) of 365 and 370 is 5.

GCF(365,370) = 5

We will now calculate the prime factors of 365 and 370, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 365 and 370.

How to find the GCF of 365 and 370?

We will first find the prime factorization of 365 and 370. After we will calculate the factors of 365 and 370 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 370

Prime factors of 370 are 2, 5, 37. Prime factorization of 370 in exponential form is:

370 = 2¹ × 5¹ × 37¹

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 370

List of positive integer factors of 370 that divides 365 without a remainder.

1, 2, 5, 10, 37, 74, 185

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 365 and 370. The biggest common factor number is the GCF number.
So the greatest common factor 365 and 370 is 5.

Also check out the Least Common Multiple of 365 and 370