What is the Greatest Common Factor of 21100 and 21114?

Greatest common factor (GCF) of 21100 and 21114 is 2.

GCF(21100,21114) = 2

We will now calculate the prime factors of 21100 and 21114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21100 and 21114.

How to find the GCF of 21100 and 21114?

We will first find the prime factorization of 21100 and 21114. After we will calculate the factors of 21100 and 21114 and find the biggest common factor number .

Step-1: Prime Factorization of 21100

Prime factors of 21100 are 2, 5, 211. Prime factorization of 21100 in exponential form is:

21100 = 2² × 5² × 211¹

Step-2: Prime Factorization of 21114

Prime factors of 21114 are 2, 3, 17, 23. Prime factorization of 21114 in exponential form is:

21114 = 2¹ × 3³ × 17¹ × 23¹

Step-3: Factors of 21100

List of positive integer factors of 21100 that divides 21100 without a remainder.

1, 2, 4, 5, 10, 20, 25, 50, 100, 211, 422, 844, 1055, 2110, 4220, 5275, 10550

Step-4: Factors of 21114

List of positive integer factors of 21114 that divides 21100 without a remainder.

1, 2, 3, 6, 9, 17, 18, 23, 27, 34, 46, 51, 54, 69, 102, 138, 153, 207, 306, 391, 414, 459, 621, 782, 918, 1173, 1242, 2346, 3519, 7038, 10557

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21100 and 21114. The biggest common factor number is the GCF number.
So the greatest common factor 21100 and 21114 is 2.

Also check out the Least Common Multiple of 21100 and 21114