What is the Greatest Common Factor of 14675 and 14680?

Greatest common factor (GCF) of 14675 and 14680 is 5.

GCF(14675,14680) = 5

We will now calculate the prime factors of 14675 and 14680, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14675 and 14680.

How to find the GCF of 14675 and 14680?

We will first find the prime factorization of 14675 and 14680. After we will calculate the factors of 14675 and 14680 and find the biggest common factor number .

Step-1: Prime Factorization of 14675

Prime factors of 14675 are 5, 587. Prime factorization of 14675 in exponential form is:

14675 = 5² × 587¹

Step-2: Prime Factorization of 14680

Prime factors of 14680 are 2, 5, 367. Prime factorization of 14680 in exponential form is:

14680 = 2³ × 5¹ × 367¹

Step-3: Factors of 14675

List of positive integer factors of 14675 that divides 14675 without a remainder.

1, 5, 25, 587, 2935

Step-4: Factors of 14680

List of positive integer factors of 14680 that divides 14675 without a remainder.

1, 2, 4, 5, 8, 10, 20, 40, 367, 734, 1468, 1835, 2936, 3670, 7340

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14675 and 14680. The biggest common factor number is the GCF number.
So the greatest common factor 14675 and 14680 is 5.

Also check out the Least Common Multiple of 14675 and 14680