What is the Greatest Common Factor of 2140 and 2160?

Greatest common factor (GCF) of 2140 and 2160 is 20.

GCF(2140,2160) = 20

We will now calculate the prime factors of 2140 and 2160, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2140 and 2160.

How to find the GCF of 2140 and 2160?

We will first find the prime factorization of 2140 and 2160. After we will calculate the factors of 2140 and 2160 and find the biggest common factor number .

Step-1: Prime Factorization of 2140

Prime factors of 2140 are 2, 5, 107. Prime factorization of 2140 in exponential form is:

2140 = 2² × 5¹ × 107¹

Step-2: 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-3: Factors of 2140

List of positive integer factors of 2140 that divides 2140 without a remainder.

1, 2, 4, 5, 10, 20, 107, 214, 428, 535, 1070

Step-4: Factors of 2160

List of positive integer factors of 2160 that divides 2140 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2140 and 2160. The biggest common factor number is the GCF number.
So the greatest common factor 2140 and 2160 is 20.

Also check out the Least Common Multiple of 2140 and 2160