What is the Greatest Common Factor of 10175 and 10180?

Greatest common factor (GCF) of 10175 and 10180 is 5.

GCF(10175,10180) = 5

We will now calculate the prime factors of 10175 and 10180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 10175 and 10180.

How to find the GCF of 10175 and 10180?

We will first find the prime factorization of 10175 and 10180. After we will calculate the factors of 10175 and 10180 and find the biggest common factor number .

Step-1: Prime Factorization of 10175

Prime factors of 10175 are 5, 11, 37. Prime factorization of 10175 in exponential form is:

10175 = 5² × 11¹ × 37¹

Step-2: Prime Factorization of 10180

Prime factors of 10180 are 2, 5, 509. Prime factorization of 10180 in exponential form is:

10180 = 2² × 5¹ × 509¹

Step-3: Factors of 10175

List of positive integer factors of 10175 that divides 10175 without a remainder.

1, 5, 11, 25, 37, 55, 185, 275, 407, 925, 2035

Step-4: Factors of 10180

List of positive integer factors of 10180 that divides 10175 without a remainder.

1, 2, 4, 5, 10, 20, 509, 1018, 2036, 2545, 5090

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 10175 and 10180. The biggest common factor number is the GCF number.
So the greatest common factor 10175 and 10180 is 5.

Also check out the Least Common Multiple of 10175 and 10180