What is the Greatest Common Factor of 2160 and 2180?

Greatest common factor (GCF) of 2160 and 2180 is 20.

GCF(2160,2180) = 20

We will now calculate the prime factors of 2160 and 2180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2160 and 2180.

How to find the GCF of 2160 and 2180?

We will first find the prime factorization of 2160 and 2180. After we will calculate the factors of 2160 and 2180 and find the biggest common factor number .

Step-1: Prime Factorization of 2160

Prime factors of 2160 are 2, 3, 5. Prime factorization of 2160 in exponential form is:

2160 = 2⁴ × 3³ × 5¹

Step-2: Prime Factorization of 2180

Prime factors of 2180 are 2, 5, 109. Prime factorization of 2180 in exponential form is:

2180 = 2² × 5¹ × 109¹

Step-3: Factors of 2160

List of positive integer factors of 2160 that divides 2160 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 90, 108, 120, 135, 144, 180, 216, 240, 270, 360, 432, 540, 720, 1080

Step-4: Factors of 2180

List of positive integer factors of 2180 that divides 2160 without a remainder.

1, 2, 4, 5, 10, 20, 109, 218, 436, 545, 1090

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2160 and 2180. The biggest common factor number is the GCF number.
So the greatest common factor 2160 and 2180 is 20.

Also check out the Least Common Multiple of 2160 and 2180