What is the Greatest Common Factor of 14705 and 14720?

Greatest common factor (GCF) of 14705 and 14720 is 5.

GCF(14705,14720) = 5

We will now calculate the prime factors of 14705 and 14720, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14705 and 14720.

How to find the GCF of 14705 and 14720?

We will first find the prime factorization of 14705 and 14720. After we will calculate the factors of 14705 and 14720 and find the biggest common factor number .

Step-1: Prime Factorization of 14705

Prime factors of 14705 are 5, 17, 173. Prime factorization of 14705 in exponential form is:

14705 = 5¹ × 17¹ × 173¹

Step-2: Prime Factorization of 14720

Prime factors of 14720 are 2, 5, 23. Prime factorization of 14720 in exponential form is:

14720 = 2⁷ × 5¹ × 23¹

Step-3: Factors of 14705

List of positive integer factors of 14705 that divides 14705 without a remainder.

1, 5, 17, 85, 173, 865, 2941

Step-4: Factors of 14720

List of positive integer factors of 14720 that divides 14705 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 23, 32, 40, 46, 64, 80, 92, 115, 128, 160, 184, 230, 320, 368, 460, 640, 736, 920, 1472, 1840, 2944, 3680, 7360

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14705 and 14720. The biggest common factor number is the GCF number.
So the greatest common factor 14705 and 14720 is 5.

Also check out the Least Common Multiple of 14705 and 14720