What is the Greatest Common Factor of 2100 and 2106?

Greatest common factor (GCF) of 2100 and 2106 is 6.

GCF(2100,2106) = 6

We will now calculate the prime factors of 2100 and 2106, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2100 and 2106.

How to find the GCF of 2100 and 2106?

We will first find the prime factorization of 2100 and 2106. After we will calculate the factors of 2100 and 2106 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 2106

Prime factors of 2106 are 2, 3, 13. Prime factorization of 2106 in exponential form is:

2106 = 2¹ × 3⁴ × 13¹

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 2106

List of positive integer factors of 2106 that divides 2100 without a remainder.

1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 81, 117, 162, 234, 351, 702, 1053

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 2100 and 2106. The biggest common factor number is the GCF number.
So the greatest common factor 2100 and 2106 is 6.

Also check out the Least Common Multiple of 2100 and 2106