What is the Greatest Common Factor of 2085 and 2100?

Greatest common factor (GCF) of 2085 and 2100 is 15.

GCF(2085,2100) = 15

We will now calculate the prime factors of 2085 and 2100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2085 and 2100.

How to find the GCF of 2085 and 2100?

We will first find the prime factorization of 2085 and 2100. After we will calculate the factors of 2085 and 2100 and find the biggest common factor number .

Step-1: Prime Factorization of 2085

Prime factors of 2085 are 3, 5, 139. Prime factorization of 2085 in exponential form is:

2085 = 3¹ × 5¹ × 139¹

Step-2: 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-3: Factors of 2085

List of positive integer factors of 2085 that divides 2085 without a remainder.

1, 3, 5, 15, 139, 417, 695

Step-4: Factors of 2100

List of positive integer factors of 2100 that divides 2085 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2085 and 2100. The biggest common factor number is the GCF number.
So the greatest common factor 2085 and 2100 is 15.

Also check out the Least Common Multiple of 2085 and 2100