What is the Greatest Common Factor of 14732 and 14742?

Greatest common factor (GCF) of 14732 and 14742 is 2.

GCF(14732,14742) = 2

We will now calculate the prime factors of 14732 and 14742, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14732 and 14742.

How to find the GCF of 14732 and 14742?

We will first find the prime factorization of 14732 and 14742. After we will calculate the factors of 14732 and 14742 and find the biggest common factor number .

Step-1: Prime Factorization of 14732

Prime factors of 14732 are 2, 29, 127. Prime factorization of 14732 in exponential form is:

14732 = 2² × 29¹ × 127¹

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 14732

List of positive integer factors of 14732 that divides 14732 without a remainder.

1, 2, 4, 29, 58, 116, 127, 254, 508, 3683, 7366

Step-4: Factors of 14742

List of positive integer factors of 14742 that divides 14732 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 14732 and 14742. The biggest common factor number is the GCF number.
So the greatest common factor 14732 and 14742 is 2.

Also check out the Least Common Multiple of 14732 and 14742