What is the Greatest Common Factor of 2100 and 2115?

Greatest common factor (GCF) of 2100 and 2115 is 15.

GCF(2100,2115) = 15

We will now calculate the prime factors of 2100 and 2115, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2100 and 2115.

How to find the GCF of 2100 and 2115?

We will first find the prime factorization of 2100 and 2115. After we will calculate the factors of 2100 and 2115 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 2115

Prime factors of 2115 are 3, 5, 47. Prime factorization of 2115 in exponential form is:

2115 = 3² × 5¹ × 47¹

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 2115

List of positive integer factors of 2115 that divides 2100 without a remainder.

1, 3, 5, 9, 15, 45, 47, 141, 235, 423, 705

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2100 and 2115. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2115 is 15.

Also check out the Least Common Multiple of 2100 and 2115