What is the Greatest Common Factor of 20175 and 20184?

Greatest common factor (GCF) of 20175 and 20184 is 3.

GCF(20175,20184) = 3

We will now calculate the prime factors of 20175 and 20184, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20175 and 20184.

How to find the GCF of 20175 and 20184?

We will first find the prime factorization of 20175 and 20184. After we will calculate the factors of 20175 and 20184 and find the biggest common factor number .

Step-1: Prime Factorization of 20175

Prime factors of 20175 are 3, 5, 269. Prime factorization of 20175 in exponential form is:

20175 = 3¹ × 5² × 269¹

Step-2: Prime Factorization of 20184

Prime factors of 20184 are 2, 3, 29. Prime factorization of 20184 in exponential form is:

20184 = 2³ × 3¹ × 29²

Step-3: Factors of 20175

List of positive integer factors of 20175 that divides 20175 without a remainder.

1, 3, 5, 15, 25, 75, 269, 807, 1345, 4035, 6725

Step-4: Factors of 20184

List of positive integer factors of 20184 that divides 20175 without a remainder.

1, 2, 3, 4, 6, 8, 12, 24, 29, 58, 87, 116, 174, 232, 348, 696, 841, 1682, 2523, 3364, 5046, 6728, 10092

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20175 and 20184. The biggest common factor number is the GCF number.
So the greatest common factor 20175 and 20184 is 3.

Also check out the Least Common Multiple of 20175 and 20184