What is the Greatest Common Factor of 14287 and 14300?

Greatest common factor (GCF) of 14287 and 14300 is 13.

GCF(14287,14300) = 13

We will now calculate the prime factors of 14287 and 14300, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14287 and 14300.

How to find the GCF of 14287 and 14300?

We will first find the prime factorization of 14287 and 14300. After we will calculate the factors of 14287 and 14300 and find the biggest common factor number .

Step-1: Prime Factorization of 14287

Prime factors of 14287 are 7, 13, 157. Prime factorization of 14287 in exponential form is:

14287 = 7¹ × 13¹ × 157¹

Step-2: Prime Factorization of 14300

Prime factors of 14300 are 2, 5, 11, 13. Prime factorization of 14300 in exponential form is:

14300 = 2² × 5² × 11¹ × 13¹

Step-3: Factors of 14287

List of positive integer factors of 14287 that divides 14287 without a remainder.

1, 7, 13, 91, 157, 1099, 2041

Step-4: Factors of 14300

List of positive integer factors of 14300 that divides 14287 without a remainder.

1, 2, 4, 5, 10, 11, 13, 20, 22, 25, 26, 44, 50, 52, 55, 65, 100, 110, 130, 143, 220, 260, 275, 286, 325, 550, 572, 650, 715, 1100, 1300, 1430, 2860, 3575, 7150

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14287 and 14300. The biggest common factor number is the GCF number.
So the greatest common factor 14287 and 14300 is 13.

Also check out the Least Common Multiple of 14287 and 14300