What is the Greatest Common Factor of 14100 and 14109?

Greatest common factor (GCF) of 14100 and 14109 is 3.

GCF(14100,14109) = 3

We will now calculate the prime factors of 14100 and 14109, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14100 and 14109.

How to find the GCF of 14100 and 14109?

We will first find the prime factorization of 14100 and 14109. After we will calculate the factors of 14100 and 14109 and find the biggest common factor number .

Step-1: Prime Factorization of 14100

Prime factors of 14100 are 2, 3, 5, 47. Prime factorization of 14100 in exponential form is:

14100 = 2² × 3¹ × 5² × 47¹

Step-2: Prime Factorization of 14109

Prime factors of 14109 are 3, 4703. Prime factorization of 14109 in exponential form is:

14109 = 3¹ × 4703¹

Step-3: Factors of 14100

List of positive integer factors of 14100 that divides 14100 without a remainder.

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 47, 50, 60, 75, 94, 100, 141, 150, 188, 235, 282, 300, 470, 564, 705, 940, 1175, 1410, 2350, 2820, 3525, 4700, 7050

Step-4: Factors of 14109

List of positive integer factors of 14109 that divides 14100 without a remainder.

1, 3, 4703

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14100 and 14109. The biggest common factor number is the GCF number.
So the greatest common factor 14100 and 14109 is 3.

Also check out the Least Common Multiple of 14100 and 14109