What is the Greatest Common Factor of 14724 and 14742?

Greatest common factor (GCF) of 14724 and 14742 is 18.

GCF(14724,14742) = 18

We will now calculate the prime factors of 14724 and 14742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14724 and 14742.

How to find the GCF of 14724 and 14742?

We will first find the prime factorization of 14724 and 14742. After we will calculate the factors of 14724 and 14742 and find the biggest common factor number .

Step-1: Prime Factorization of 14724

Prime factors of 14724 are 2, 3, 409. Prime factorization of 14724 in exponential form is:

14724 = 2² × 3² × 409¹

Step-2: Prime Factorization of 14742

Prime factors of 14742 are 2, 3, 7, 13. Prime factorization of 14742 in exponential form is:

14742 = 2¹ × 3⁴ × 7¹ × 13¹

Step-3: Factors of 14724

List of positive integer factors of 14724 that divides 14724 without a remainder.

1, 2, 3, 4, 6, 9, 12, 18, 36, 409, 818, 1227, 1636, 2454, 3681, 4908, 7362

Step-4: Factors of 14742

List of positive integer factors of 14742 that divides 14724 without a remainder.

1, 2, 3, 6, 7, 9, 13, 14, 18, 21, 26, 27, 39, 42, 54, 63, 78, 81, 91, 117, 126, 162, 182, 189, 234, 273, 351, 378, 546, 567, 702, 819, 1053, 1134, 1638, 2106, 2457, 4914, 7371

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14724 and 14742. The biggest common factor number is the GCF number.
So the greatest common factor 14724 and 14742 is 18.

Also check out the Least Common Multiple of 14724 and 14742