What is the Greatest Common Factor of 2100 and 2109?

Greatest common factor (GCF) of 2100 and 2109 is 3.

GCF(2100,2109) = 3

We will now calculate the prime factors of 2100 and 2109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2100 and 2109.

How to find the GCF of 2100 and 2109?

We will first find the prime factorization of 2100 and 2109. After we will calculate the factors of 2100 and 2109 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 2109

Prime factors of 2109 are 3, 19, 37. Prime factorization of 2109 in exponential form is:

2109 = 3¹ × 19¹ × 37¹

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 2109

List of positive integer factors of 2109 that divides 2100 without a remainder.

1, 3, 19, 37, 57, 111, 703

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2100 and 2109. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2109 is 3.

Also check out the Least Common Multiple of 2100 and 2109