What is the Greatest Common Factor of 14742 and 14756?

Greatest common factor (GCF) of 14742 and 14756 is 14.

GCF(14742,14756) = 14

We will now calculate the prime factors of 14742 and 14756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14742 and 14756.

How to find the GCF of 14742 and 14756?

We will first find the prime factorization of 14742 and 14756. After we will calculate the factors of 14742 and 14756 and find the biggest common factor number .

Step-1: 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-2: Prime Factorization of 14756

Prime factors of 14756 are 2, 7, 17, 31. Prime factorization of 14756 in exponential form is:

14756 = 2² × 7¹ × 17¹ × 31¹

Step-3: Factors of 14742

List of positive integer factors of 14742 that divides 14742 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

Step-4: Factors of 14756

List of positive integer factors of 14756 that divides 14742 without a remainder.

1, 2, 4, 7, 14, 17, 28, 31, 34, 62, 68, 119, 124, 217, 238, 434, 476, 527, 868, 1054, 2108, 3689, 7378

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14742 and 14756. The biggest common factor number is the GCF number.
So the greatest common factor 14742 and 14756 is 14.

Also check out the Least Common Multiple of 14742 and 14756