What is the Greatest Common Factor of 2100 and 2112?

Greatest common factor (GCF) of 2100 and 2112 is 12.

GCF(2100,2112) = 12

We will now calculate the prime factors of 2100 and 2112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2100 and 2112.

How to find the GCF of 2100 and 2112?

We will first find the prime factorization of 2100 and 2112. After we will calculate the factors of 2100 and 2112 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 2112

Prime factors of 2112 are 2, 3, 11. Prime factorization of 2112 in exponential form is:

2112 = 2⁶ × 3¹ × 11¹

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 2112

List of positive integer factors of 2112 that divides 2100 without a remainder.

1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 64, 66, 88, 96, 132, 176, 192, 264, 352, 528, 704, 1056

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2100 and 2112. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2112 is 12.

Also check out the Least Common Multiple of 2100 and 2112