What is the Greatest Common Factor of 21096 and 21114?

Greatest common factor (GCF) of 21096 and 21114 is 18.

GCF(21096,21114) = 18

We will now calculate the prime factors of 21096 and 21114, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21096 and 21114.

How to find the GCF of 21096 and 21114?

We will first find the prime factorization of 21096 and 21114. After we will calculate the factors of 21096 and 21114 and find the biggest common factor number .

Step-1: Prime Factorization of 21096

Prime factors of 21096 are 2, 3, 293. Prime factorization of 21096 in exponential form is:

21096 = 2³ × 3² × 293¹

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 21096

List of positive integer factors of 21096 that divides 21096 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 293, 586, 879, 1172, 1758, 2344, 2637, 3516, 5274, 7032, 10548

Step-4: Factors of 21114

List of positive integer factors of 21114 that divides 21096 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 21096 and 21114. The biggest common factor number is the GCF number.
So the greatest common factor 21096 and 21114 is 18.

Also check out the Least Common Multiple of 21096 and 21114