What is the Greatest Common Factor of 21114 and 21131?

Greatest common factor (GCF) of 21114 and 21131 is 17.

GCF(21114,21131) = 17

We will now calculate the prime factors of 21114 and 21131, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21114 and 21131.

How to find the GCF of 21114 and 21131?

We will first find the prime factorization of 21114 and 21131. After we will calculate the factors of 21114 and 21131 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 21131

Prime factors of 21131 are 11, 17, 113. Prime factorization of 21131 in exponential form is:

21131 = 11¹ × 17¹ × 113¹

Step-3: Factors of 21114

List of positive integer factors of 21114 that divides 21114 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

Step-4: Factors of 21131

List of positive integer factors of 21131 that divides 21114 without a remainder.

1, 11, 17, 113, 187, 1243, 1921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21114 and 21131. The biggest common factor number is the GCF number.
So the greatest common factor 21114 and 21131 is 17.

Also check out the Least Common Multiple of 21114 and 21131