What is the Greatest Common Factor of 2100 and 2105?

Greatest common factor (GCF) of 2100 and 2105 is 5.

GCF(2100,2105) = 5

We will now calculate the prime factors of 2100 and 2105, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2100 and 2105.

How to find the GCF of 2100 and 2105?

We will first find the prime factorization of 2100 and 2105. After we will calculate the factors of 2100 and 2105 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 2105

Prime factors of 2105 are 5, 421. Prime factorization of 2105 in exponential form is:

2105 = 5¹ × 421¹

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 2105

List of positive integer factors of 2105 that divides 2100 without a remainder.

1, 5, 421

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2100 and 2105. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2105 is 5.

Also check out the Least Common Multiple of 2100 and 2105