What is the Greatest Common Factor of 14749 and 14768?

Greatest common factor (GCF) of 14749 and 14768 is 1.

GCF(14749,14768) = 1

We will now calculate the prime factors of 14749 and 14768, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14749 and 14768.

How to find the GCF of 14749 and 14768?

We will first find the prime factorization of 14749 and 14768. After we will calculate the factors of 14749 and 14768 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 14768

Prime factors of 14768 are 2, 13, 71. Prime factorization of 14768 in exponential form is:

14768 = 2⁴ × 13¹ × 71¹

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 14768

List of positive integer factors of 14768 that divides 14749 without a remainder.

1, 2, 4, 8, 13, 16, 26, 52, 71, 104, 142, 208, 284, 568, 923, 1136, 1846, 3692, 7384

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14749 and 14768. The biggest common factor number is the GCF number.
So the greatest common factor 14749 and 14768 is 1.

Also check out the Least Common Multiple of 14749 and 14768