What is the Greatest Common Factor of 23808 and 23814?

Greatest common factor (GCF) of 23808 and 23814 is 6.

GCF(23808,23814) = 6

We will now calculate the prime factors of 23808 and 23814, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 23808 and 23814.

How to find the GCF of 23808 and 23814?

We will first find the prime factorization of 23808 and 23814. After we will calculate the factors of 23808 and 23814 and find the biggest common factor number .

Step-1: Prime Factorization of 23808

Prime factors of 23808 are 2, 3, 31. Prime factorization of 23808 in exponential form is:

23808 = 2⁸ × 3¹ × 31¹

Step-2: 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-3: Factors of 23808

List of positive integer factors of 23808 that divides 23808 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 32, 48, 62, 64, 93, 96, 124, 128, 186, 192, 248, 256, 372, 384, 496, 744, 768, 992, 1488, 1984, 2976, 3968, 5952, 7936, 11904

Step-4: Factors of 23814

List of positive integer factors of 23814 that divides 23808 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 23808 and 23814. The biggest common factor number is the GCF number.
So the greatest common factor 23808 and 23814 is 6.

Also check out the Least Common Multiple of 23808 and 23814