What is the Greatest Common Factor of 2175 and 2184?

Greatest common factor (GCF) of 2175 and 2184 is 3.

GCF(2175,2184) = 3

We will now calculate the prime factors of 2175 and 2184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2175 and 2184.

How to find the GCF of 2175 and 2184?

We will first find the prime factorization of 2175 and 2184. After we will calculate the factors of 2175 and 2184 and find the biggest common factor number .

Step-1: Prime Factorization of 2175

Prime factors of 2175 are 3, 5, 29. Prime factorization of 2175 in exponential form is:

2175 = 3¹ × 5² × 29¹

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 2175

List of positive integer factors of 2175 that divides 2175 without a remainder.

1, 3, 5, 15, 25, 29, 75, 87, 145, 435, 725

Step-4: Factors of 2184

List of positive integer factors of 2184 that divides 2175 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 2175 and 2184. The biggest common factor number is the GCF number.
So the greatest common factor 2175 and 2184 is 3.

Also check out the Least Common Multiple of 2175 and 2184