What is the Greatest Common Factor of 2160 and 2172?

Greatest common factor (GCF) of 2160 and 2172 is 12.

GCF(2160,2172) = 12

We will now calculate the prime factors of 2160 and 2172, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2160 and 2172.

How to find the GCF of 2160 and 2172?

We will first find the prime factorization of 2160 and 2172. After we will calculate the factors of 2160 and 2172 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 2172

Prime factors of 2172 are 2, 3, 181. Prime factorization of 2172 in exponential form is:

2172 = 2² × 3¹ × 181¹

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 2172

List of positive integer factors of 2172 that divides 2160 without a remainder.

1, 2, 3, 4, 6, 12, 181, 362, 543, 724, 1086

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2160 and 2172. The biggest common factor number is the GCF number.
So the greatest common factor 2160 and 2172 is 12.

Also check out the Least Common Multiple of 2160 and 2172