What is the Greatest Common Factor of 2101 and 2112?

Greatest common factor (GCF) of 2101 and 2112 is 11.

GCF(2101,2112) = 11

We will now calculate the prime factors of 2101 and 2112, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 2101 and 2112.

How to find the GCF of 2101 and 2112?

We will first find the prime factorization of 2101 and 2112. After we will calculate the factors of 2101 and 2112 and find the biggest common factor number .

Step-1: Prime Factorization of 2101

Prime factors of 2101 are 11, 191. Prime factorization of 2101 in exponential form is:

2101 = 11¹ × 191¹

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 2101

List of positive integer factors of 2101 that divides 2101 without a remainder.

1, 11, 191

Step-4: Factors of 2112

List of positive integer factors of 2112 that divides 2101 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 2101 and 2112. The biggest common factor number is the GCF number.
So the greatest common factor 2101 and 2112 is 11.

Also check out the Least Common Multiple of 2101 and 2112