What is the Greatest Common Factor of 21175 and 21180?

Greatest common factor (GCF) of 21175 and 21180 is 5.

GCF(21175,21180) = 5

We will now calculate the prime factors of 21175 and 21180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21175 and 21180.

How to find the GCF of 21175 and 21180?

We will first find the prime factorization of 21175 and 21180. After we will calculate the factors of 21175 and 21180 and find the biggest common factor number .

Step-1: Prime Factorization of 21175

Prime factors of 21175 are 5, 7, 11. Prime factorization of 21175 in exponential form is:

21175 = 5² × 7¹ × 11²

Step-2: Prime Factorization of 21180

Prime factors of 21180 are 2, 3, 5, 353. Prime factorization of 21180 in exponential form is:

21180 = 2² × 3¹ × 5¹ × 353¹

Step-3: Factors of 21175

List of positive integer factors of 21175 that divides 21175 without a remainder.

1, 5, 7, 11, 25, 35, 55, 77, 121, 175, 275, 385, 605, 847, 1925, 3025, 4235

Step-4: Factors of 21180

List of positive integer factors of 21180 that divides 21175 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 353, 706, 1059, 1412, 1765, 2118, 3530, 4236, 5295, 7060, 10590

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21175 and 21180. The biggest common factor number is the GCF number.
So the greatest common factor 21175 and 21180 is 5.

Also check out the Least Common Multiple of 21175 and 21180