What is the Greatest Common Factor of 14240 and 14256?

Greatest common factor (GCF) of 14240 and 14256 is 16.

GCF(14240,14256) = 16

We will now calculate the prime factors of 14240 and 14256, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 14240 and 14256.

How to find the GCF of 14240 and 14256?

We will first find the prime factorization of 14240 and 14256. After we will calculate the factors of 14240 and 14256 and find the biggest common factor number .

Step-1: Prime Factorization of 14240

Prime factors of 14240 are 2, 5, 89. Prime factorization of 14240 in exponential form is:

14240 = 2⁵ × 5¹ × 89¹

Step-2: Prime Factorization of 14256

Prime factors of 14256 are 2, 3, 11. Prime factorization of 14256 in exponential form is:

14256 = 2⁴ × 3⁴ × 11¹

Step-3: Factors of 14240

List of positive integer factors of 14240 that divides 14240 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 89, 160, 178, 356, 445, 712, 890, 1424, 1780, 2848, 3560, 7120

Step-4: Factors of 14256

List of positive integer factors of 14256 that divides 14240 without a remainder.

1, 2, 3, 4, 6, 8, 9, 11, 12, 16, 18, 22, 24, 27, 33, 36, 44, 48, 54, 66, 72, 81, 88, 99, 108, 132, 144, 162, 176, 198, 216, 264, 297, 324, 396, 432, 528, 594, 648, 792, 891, 1188, 1296, 1584, 1782, 2376, 3564, 4752, 7128

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 14240 and 14256. The biggest common factor number is the GCF number.
So the greatest common factor 14240 and 14256 is 16.

Also check out the Least Common Multiple of 14240 and 14256