What is the Greatest Common Factor of 360 and 368?

Greatest common factor (GCF) of 360 and 368 is 8.

GCF(360,368) = 8

We will now calculate the prime factors of 360 and 368, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 360 and 368.

How to find the GCF of 360 and 368?

We will first find the prime factorization of 360 and 368. After we will calculate the factors of 360 and 368 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 368

Prime factors of 368 are 2, 23. Prime factorization of 368 in exponential form is:

368 = 2⁴ × 23¹

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 368

List of positive integer factors of 368 that divides 360 without a remainder.

1, 2, 4, 8, 16, 23, 46, 92, 184

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 360 and 368. The biggest common factor number is the GCF number.
So the greatest common factor 360 and 368 is 8.

Also check out the Least Common Multiple of 360 and 368