What is the Greatest Common Factor of 23814 and 23828?

Greatest common factor (GCF) of 23814 and 23828 is 14.

GCF(23814,23828) = 14

We will now calculate the prime factors of 23814 and 23828, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23814 and 23828.

How to find the GCF of 23814 and 23828?

We will first find the prime factorization of 23814 and 23828. After we will calculate the factors of 23814 and 23828 and find the biggest common factor number .

Step-1: Prime Factorization of 23814

Prime factors of 23814 are 2, 3, 7. Prime factorization of 23814 in exponential form is:

23814 = 2¹ × 3⁵ × 7²

Step-2: Prime Factorization of 23828

Prime factors of 23828 are 2, 7, 23, 37. Prime factorization of 23828 in exponential form is:

23828 = 2² × 7¹ × 23¹ × 37¹

Step-3: Factors of 23814

List of positive integer factors of 23814 that divides 23814 without a remainder.

1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 49, 54, 63, 81, 98, 126, 147, 162, 189, 243, 294, 378, 441, 486, 567, 882, 1134, 1323, 1701, 2646, 3402, 3969, 7938, 11907

Step-4: Factors of 23828

List of positive integer factors of 23828 that divides 23814 without a remainder.

1, 2, 4, 7, 14, 23, 28, 37, 46, 74, 92, 148, 161, 259, 322, 518, 644, 851, 1036, 1702, 3404, 5957, 11914

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23814 and 23828. The biggest common factor number is the GCF number.
So the greatest common factor 23814 and 23828 is 14.

Also check out the Least Common Multiple of 23814 and 23828