What is the Greatest Common Factor of 2170 and 2188?

Greatest common factor (GCF) of 2170 and 2188 is 2.

GCF(2170,2188) = 2

We will now calculate the prime factors of 2170 and 2188, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2170 and 2188.

How to find the GCF of 2170 and 2188?

We will first find the prime factorization of 2170 and 2188. After we will calculate the factors of 2170 and 2188 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 2188

Prime factors of 2188 are 2, 547. Prime factorization of 2188 in exponential form is:

2188 = 2² × 547¹

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 2188

List of positive integer factors of 2188 that divides 2170 without a remainder.

1, 2, 4, 547, 1094

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2170 and 2188. The biggest common factor number is the GCF number.
So the greatest common factor 2170 and 2188 is 2.

Also check out the Least Common Multiple of 2170 and 2188