What is the Greatest Common Factor of 360 and 364?

Greatest common factor (GCF) of 360 and 364 is 4.

GCF(360,364) = 4

We will now calculate the prime factors of 360 and 364, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 360 and 364.

How to find the GCF of 360 and 364?

We will first find the prime factorization of 360 and 364. After we will calculate the factors of 360 and 364 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 364

Prime factors of 364 are 2, 7, 13. Prime factorization of 364 in exponential form is:

364 = 2² × 7¹ × 13¹

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 364

List of positive integer factors of 364 that divides 360 without a remainder.

1, 2, 4, 7, 13, 14, 26, 28, 52, 91, 182

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 360 and 364. The biggest common factor number is the GCF number.
So the greatest common factor 360 and 364 is 4.

Also check out the Least Common Multiple of 360 and 364