What is the Greatest Common Factor of 14742 and 14761?

Greatest common factor (GCF) of 14742 and 14761 is 1.

GCF(14742,14761) = 1

We will now calculate the prime factors of 14742 and 14761, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14742 and 14761.

How to find the GCF of 14742 and 14761?

We will first find the prime factorization of 14742 and 14761. After we will calculate the factors of 14742 and 14761 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 14761

Prime factors of 14761 are 29, 509. Prime factorization of 14761 in exponential form is:

14761 = 29¹ × 509¹

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 14761

List of positive integer factors of 14761 that divides 14742 without a remainder.

1, 29, 509

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14742 and 14761. The biggest common factor number is the GCF number.
So the greatest common factor 14742 and 14761 is 1.

Also check out the Least Common Multiple of 14742 and 14761