What is the Greatest Common Factor of 14075 and 14080?

Greatest common factor (GCF) of 14075 and 14080 is 5.

GCF(14075,14080) = 5

We will now calculate the prime factors of 14075 and 14080, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14075 and 14080.

How to find the GCF of 14075 and 14080?

We will first find the prime factorization of 14075 and 14080. After we will calculate the factors of 14075 and 14080 and find the biggest common factor number .

Step-1: Prime Factorization of 14075

Prime factors of 14075 are 5, 563. Prime factorization of 14075 in exponential form is:

14075 = 5² × 563¹

Step-2: 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-3: Factors of 14075

List of positive integer factors of 14075 that divides 14075 without a remainder.

1, 5, 25, 563, 2815

Step-4: Factors of 14080

List of positive integer factors of 14080 that divides 14075 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

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14075 and 14080. The biggest common factor number is the GCF number.
So the greatest common factor 14075 and 14080 is 5.

Also check out the Least Common Multiple of 14075 and 14080