What is the Greatest Common Factor of 14665 and 14674?

Greatest common factor (GCF) of 14665 and 14674 is 1.

GCF(14665,14674) = 1

We will now calculate the prime factors of 14665 and 14674, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14665 and 14674.

How to find the GCF of 14665 and 14674?

We will first find the prime factorization of 14665 and 14674. After we will calculate the factors of 14665 and 14674 and find the biggest common factor number .

Step-1: Prime Factorization of 14665

Prime factors of 14665 are 5, 7, 419. Prime factorization of 14665 in exponential form is:

14665 = 5¹ × 7¹ × 419¹

Step-2: Prime Factorization of 14674

Prime factors of 14674 are 2, 11, 23, 29. Prime factorization of 14674 in exponential form is:

14674 = 2¹ × 11¹ × 23¹ × 29¹

Step-3: Factors of 14665

List of positive integer factors of 14665 that divides 14665 without a remainder.

1, 5, 7, 35, 419, 2095, 2933

Step-4: Factors of 14674

List of positive integer factors of 14674 that divides 14665 without a remainder.

1, 2, 11, 22, 23, 29, 46, 58, 253, 319, 506, 638, 667, 1334, 7337

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14665 and 14674. The biggest common factor number is the GCF number.
So the greatest common factor 14665 and 14674 is 1.

Also check out the Least Common Multiple of 14665 and 14674