What is the Greatest Common Factor of 14739 and 14756?

Greatest common factor (GCF) of 14739 and 14756 is 17.

GCF(14739,14756) = 17

We will now calculate the prime factors of 14739 and 14756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14739 and 14756.

How to find the GCF of 14739 and 14756?

We will first find the prime factorization of 14739 and 14756. After we will calculate the factors of 14739 and 14756 and find the biggest common factor number .

Step-1: Prime Factorization of 14739

Prime factors of 14739 are 3, 17. Prime factorization of 14739 in exponential form is:

14739 = 3¹ × 17³

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 14739

List of positive integer factors of 14739 that divides 14739 without a remainder.

1, 3, 17, 51, 289, 867, 4913

Step-4: Factors of 14756

List of positive integer factors of 14756 that divides 14739 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 14739 and 14756. The biggest common factor number is the GCF number.
So the greatest common factor 14739 and 14756 is 17.

Also check out the Least Common Multiple of 14739 and 14756