What is the Greatest Common Factor of 2100 and 2114?

Greatest common factor (GCF) of 2100 and 2114 is 14.

GCF(2100,2114) = 14

We will now calculate the prime factors of 2100 and 2114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2100 and 2114.

How to find the GCF of 2100 and 2114?

We will first find the prime factorization of 2100 and 2114. After we will calculate the factors of 2100 and 2114 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 2114

Prime factors of 2114 are 2, 7, 151. Prime factorization of 2114 in exponential form is:

2114 = 2¹ × 7¹ × 151¹

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 2114

List of positive integer factors of 2114 that divides 2100 without a remainder.

1, 2, 7, 14, 151, 302, 1057

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2100 and 2114. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2114 is 14.

Also check out the Least Common Multiple of 2100 and 2114