What is the Greatest Common Factor of 2170 and 2185?

Greatest common factor (GCF) of 2170 and 2185 is 5.

GCF(2170,2185) = 5

We will now calculate the prime factors of 2170 and 2185, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2170 and 2185.

How to find the GCF of 2170 and 2185?

We will first find the prime factorization of 2170 and 2185. After we will calculate the factors of 2170 and 2185 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 2185

Prime factors of 2185 are 5, 19, 23. Prime factorization of 2185 in exponential form is:

2185 = 5¹ × 19¹ × 23¹

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 2185

List of positive integer factors of 2185 that divides 2170 without a remainder.

1, 5, 19, 23, 95, 115, 437

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2170 and 2185. The biggest common factor number is the GCF number.
So the greatest common factor 2170 and 2185 is 5.

Also check out the Least Common Multiple of 2170 and 2185