What is the Greatest Common Factor of 14080 and 14100?

Greatest common factor (GCF) of 14080 and 14100 is 20.

GCF(14080,14100) = 20

We will now calculate the prime factors of 14080 and 14100, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14080 and 14100.

How to find the GCF of 14080 and 14100?

We will first find the prime factorization of 14080 and 14100. After we will calculate the factors of 14080 and 14100 and find the biggest common factor number .

Step-1: Prime Factorization of 14080

Prime factors of 14080 are 2, 5, 11. Prime factorization of 14080 in exponential form is:

14080 = 2⁸ × 5¹ × 11¹

Step-2: 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-3: Factors of 14080

List of positive integer factors of 14080 that divides 14080 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 64, 80, 88, 110, 128, 160, 176, 220, 256, 320, 352, 440, 640, 704, 880, 1280, 1408, 1760, 2816, 3520, 7040

Step-4: Factors of 14100

List of positive integer factors of 14100 that divides 14080 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14080 and 14100. The biggest common factor number is the GCF number.
So the greatest common factor 14080 and 14100 is 20.

Also check out the Least Common Multiple of 14080 and 14100