What is the Greatest Common Factor of 2100 and 2110?

Greatest common factor (GCF) of 2100 and 2110 is 10.

GCF(2100,2110) = 10

We will now calculate the prime factors of 2100 and 2110, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2100 and 2110.

How to find the GCF of 2100 and 2110?

We will first find the prime factorization of 2100 and 2110. After we will calculate the factors of 2100 and 2110 and find the biggest common factor number .

Step-1: Prime Factorization of 2100

Prime factors of 2100 are 2, 3, 5, 7. Prime factorization of 2100 in exponential form is:

2100 = 2² × 3¹ × 5² × 7¹

Step-2: Prime Factorization of 2110

Prime factors of 2110 are 2, 5, 211. Prime factorization of 2110 in exponential form is:

2110 = 2¹ × 5¹ × 211¹

Step-3: Factors of 2100

List of positive integer factors of 2100 that divides 2100 without a remainder.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 25, 28, 30, 35, 42, 50, 60, 70, 75, 84, 100, 105, 140, 150, 175, 210, 300, 350, 420, 525, 700, 1050

Step-4: Factors of 2110

List of positive integer factors of 2110 that divides 2100 without a remainder.

1, 2, 5, 10, 211, 422, 1055

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2100 and 2110. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2110 is 10.

Also check out the Least Common Multiple of 2100 and 2110