What is the Greatest Common Factor of 2170 and 2180?

Greatest common factor (GCF) of 2170 and 2180 is 10.

GCF(2170,2180) = 10

We will now calculate the prime factors of 2170 and 2180, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2170 and 2180.

How to find the GCF of 2170 and 2180?

We will first find the prime factorization of 2170 and 2180. After we will calculate the factors of 2170 and 2180 and find the biggest common factor number .

Step-1: Prime Factorization of 2170

Prime factors of 2170 are 2, 5, 7, 31. Prime factorization of 2170 in exponential form is:

2170 = 2¹ × 5¹ × 7¹ × 31¹

Step-2: Prime Factorization of 2180

Prime factors of 2180 are 2, 5, 109. Prime factorization of 2180 in exponential form is:

2180 = 2² × 5¹ × 109¹

Step-3: Factors of 2170

List of positive integer factors of 2170 that divides 2170 without a remainder.

1, 2, 5, 7, 10, 14, 31, 35, 62, 70, 155, 217, 310, 434, 1085

Step-4: Factors of 2180

List of positive integer factors of 2180 that divides 2170 without a remainder.

1, 2, 4, 5, 10, 20, 109, 218, 436, 545, 1090

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2170 and 2180. The biggest common factor number is the GCF number.
So the greatest common factor 2170 and 2180 is 10.

Also check out the Least Common Multiple of 2170 and 2180