What is the Greatest Common Factor of 14674 and 14688?

Greatest common factor (GCF) of 14674 and 14688 is 2.

GCF(14674,14688) = 2

We will now calculate the prime factors of 14674 and 14688, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14674 and 14688.

How to find the GCF of 14674 and 14688?

We will first find the prime factorization of 14674 and 14688. After we will calculate the factors of 14674 and 14688 and find the biggest common factor number .

Step-1: Prime Factorization of 14674

Prime factors of 14674 are 2, 11, 23, 29. Prime factorization of 14674 in exponential form is:

14674 = 2¹ × 11¹ × 23¹ × 29¹

Step-2: Prime Factorization of 14688

Prime factors of 14688 are 2, 3, 17. Prime factorization of 14688 in exponential form is:

14688 = 2⁵ × 3³ × 17¹

Step-3: Factors of 14674

List of positive integer factors of 14674 that divides 14674 without a remainder.

1, 2, 11, 22, 23, 29, 46, 58, 253, 319, 506, 638, 667, 1334, 7337

Step-4: Factors of 14688

List of positive integer factors of 14688 that divides 14674 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 27, 32, 34, 36, 48, 51, 54, 68, 72, 96, 102, 108, 136, 144, 153, 204, 216, 272, 288, 306, 408, 432, 459, 544, 612, 816, 864, 918, 1224, 1632, 1836, 2448, 3672, 4896, 7344

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14674 and 14688. The biggest common factor number is the GCF number.
So the greatest common factor 14674 and 14688 is 2.

Also check out the Least Common Multiple of 14674 and 14688