What is the Greatest Common Factor of 38175 and 38180?

Greatest common factor (GCF) of 38175 and 38180 is 5.

GCF(38175,38180) = 5

We will now calculate the prime factors of 38175 and 38180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 38175 and 38180.

How to find the GCF of 38175 and 38180?

We will first find the prime factorization of 38175 and 38180. After we will calculate the factors of 38175 and 38180 and find the biggest common factor number .

Step-1: Prime Factorization of 38175

Prime factors of 38175 are 3, 5, 509. Prime factorization of 38175 in exponential form is:

38175 = 3¹ × 5² × 509¹

Step-2: Prime Factorization of 38180

Prime factors of 38180 are 2, 5, 23, 83. Prime factorization of 38180 in exponential form is:

38180 = 2² × 5¹ × 23¹ × 83¹

Step-3: Factors of 38175

List of positive integer factors of 38175 that divides 38175 without a remainder.

1, 3, 5, 15, 25, 75, 509, 1527, 2545, 7635, 12725

Step-4: Factors of 38180

List of positive integer factors of 38180 that divides 38175 without a remainder.

1, 2, 4, 5, 10, 20, 23, 46, 83, 92, 115, 166, 230, 332, 415, 460, 830, 1660, 1909, 3818, 7636, 9545, 19090

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 38175 and 38180. The biggest common factor number is the GCF number.
So the greatest common factor 38175 and 38180 is 5.

Also check out the Least Common Multiple of 38175 and 38180