What is the Greatest Common Factor of 14749 and 14766?

Greatest common factor (GCF) of 14749 and 14766 is 1.

GCF(14749,14766) = 1

We will now calculate the prime factors of 14749 and 14766, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14749 and 14766.

How to find the GCF of 14749 and 14766?

We will first find the prime factorization of 14749 and 14766. After we will calculate the factors of 14749 and 14766 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 14766

Prime factors of 14766 are 2, 3, 23, 107. Prime factorization of 14766 in exponential form is:

14766 = 2¹ × 3¹ × 23¹ × 107¹

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 14766

List of positive integer factors of 14766 that divides 14749 without a remainder.

1, 2, 3, 6, 23, 46, 69, 107, 138, 214, 321, 642, 2461, 4922, 7383

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14749 and 14766. The biggest common factor number is the GCF number.
So the greatest common factor 14749 and 14766 is 1.

Also check out the Least Common Multiple of 14749 and 14766