What is the Greatest Common Factor of 14749 and 14756?

Greatest common factor (GCF) of 14749 and 14756 is 7.

GCF(14749,14756) = 7

We will now calculate the prime factors of 14749 and 14756, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14749 and 14756.

How to find the GCF of 14749 and 14756?

We will first find the prime factorization of 14749 and 14756. After we will calculate the factors of 14749 and 14756 and find the biggest common factor number .

Step-1: Prime Factorization of 14749

Prime factors of 14749 are 7, 43. Prime factorization of 14749 in exponential form is:

14749 = 7³ × 43¹

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 14749

List of positive integer factors of 14749 that divides 14749 without a remainder.

1, 7, 43, 49, 301, 343, 2107

Step-4: Factors of 14756

List of positive integer factors of 14756 that divides 14749 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 14749 and 14756. The biggest common factor number is the GCF number.
So the greatest common factor 14749 and 14756 is 7.

Also check out the Least Common Multiple of 14749 and 14756