What is the Greatest Common Factor of 2160 and 2170?

Greatest common factor (GCF) of 2160 and 2170 is 10.

GCF(2160,2170) = 10

We will now calculate the prime factors of 2160 and 2170, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2160 and 2170.

How to find the GCF of 2160 and 2170?

We will first find the prime factorization of 2160 and 2170. After we will calculate the factors of 2160 and 2170 and find the biggest common factor number .

Step-1: Prime Factorization of 2160

Prime factors of 2160 are 2, 3, 5. Prime factorization of 2160 in exponential form is:

2160 = 2⁴ × 3³ × 5¹

Step-2: 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-3: Factors of 2160

List of positive integer factors of 2160 that divides 2160 without a remainder.

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 36, 40, 45, 48, 54, 60, 72, 80, 90, 108, 120, 135, 144, 180, 216, 240, 270, 360, 432, 540, 720, 1080

Step-4: Factors of 2170

List of positive integer factors of 2170 that divides 2160 without a remainder.

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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2160 and 2170. The biggest common factor number is the GCF number.
So the greatest common factor 2160 and 2170 is 10.

Also check out the Least Common Multiple of 2160 and 2170