What is the Greatest Common Factor of 2100 and 2116?

Greatest common factor (GCF) of 2100 and 2116 is 4.

GCF(2100,2116) = 4

We will now calculate the prime factors of 2100 and 2116, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2100 and 2116.

How to find the GCF of 2100 and 2116?

We will first find the prime factorization of 2100 and 2116. After we will calculate the factors of 2100 and 2116 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 2116

Prime factors of 2116 are 2, 23. Prime factorization of 2116 in exponential form is:

2116 = 2² × 23²

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 2116

List of positive integer factors of 2116 that divides 2100 without a remainder.

1, 2, 4, 23, 46, 92, 529, 1058

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2100 and 2116. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2116 is 4.

Also check out the Least Common Multiple of 2100 and 2116