What is the Greatest Common Factor of 2172 and 2184?

Greatest common factor (GCF) of 2172 and 2184 is 12.

GCF(2172,2184) = 12

We will now calculate the prime factors of 2172 and 2184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2172 and 2184.

How to find the GCF of 2172 and 2184?

We will first find the prime factorization of 2172 and 2184. After we will calculate the factors of 2172 and 2184 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 2184

Prime factors of 2184 are 2, 3, 7, 13. Prime factorization of 2184 in exponential form is:

2184 = 2³ × 3¹ × 7¹ × 13¹

Step-3: Factors of 2172

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

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

Step-4: Factors of 2184

List of positive integer factors of 2184 that divides 2172 without a remainder.

1, 2, 3, 4, 6, 7, 8, 12, 13, 14, 21, 24, 26, 28, 39, 42, 52, 56, 78, 84, 91, 104, 156, 168, 182, 273, 312, 364, 546, 728, 1092

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2172 and 2184. The biggest common factor number is the GCF number.
So the greatest common factor 2172 and 2184 is 12.

Also check out the Least Common Multiple of 2172 and 2184