What is the Greatest Common Factor of 14749 and 14763?

Greatest common factor (GCF) of 14749 and 14763 is 7.

GCF(14749,14763) = 7

We will now calculate the prime factors of 14749 and 14763, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14749 and 14763.

How to find the GCF of 14749 and 14763?

We will first find the prime factorization of 14749 and 14763. After we will calculate the factors of 14749 and 14763 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 14763

Prime factors of 14763 are 3, 7, 19, 37. Prime factorization of 14763 in exponential form is:

14763 = 3¹ × 7¹ × 19¹ × 37¹

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 14763

List of positive integer factors of 14763 that divides 14749 without a remainder.

1, 3, 7, 19, 21, 37, 57, 111, 133, 259, 399, 703, 777, 2109, 4921

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14749 and 14763. The biggest common factor number is the GCF number.
So the greatest common factor 14749 and 14763 is 7.

Also check out the Least Common Multiple of 14749 and 14763