What is the Greatest Common Factor of 360 and 365?

Greatest common factor (GCF) of 360 and 365 is 5.

GCF(360,365) = 5

We will now calculate the prime factors of 360 and 365, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 360 and 365.

How to find the GCF of 360 and 365?

We will first find the prime factorization of 360 and 365. After we will calculate the factors of 360 and 365 and find the biggest common factor number .

Step-1: Prime Factorization of 360

Prime factors of 360 are 2, 3, 5. Prime factorization of 360 in exponential form is:

360 = 2³ × 3² × 5¹

Step-2: Prime Factorization of 365

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

365 = 5¹ × 73¹

Step-3: Factors of 360

List of positive integer factors of 360 that divides 360 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180

Step-4: Factors of 365

List of positive integer factors of 365 that divides 360 without a remainder.

1, 5, 73

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 360 and 365. The biggest common factor number is the GCF number.
So the greatest common factor 360 and 365 is 5.

Also check out the Least Common Multiple of 360 and 365