What is the Greatest Common Factor of 17856 and 17872?

Greatest common factor (GCF) of 17856 and 17872 is 16.

GCF(17856,17872) = 16

We will now calculate the prime factors of 17856 and 17872, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17856 and 17872.

How to find the GCF of 17856 and 17872?

We will first find the prime factorization of 17856 and 17872. After we will calculate the factors of 17856 and 17872 and find the biggest common factor number .

Step-1: Prime Factorization of 17856

Prime factors of 17856 are 2, 3, 31. Prime factorization of 17856 in exponential form is:

17856 = 2⁶ × 3² × 31¹

Step-2: Prime Factorization of 17872

Prime factors of 17872 are 2, 1117. Prime factorization of 17872 in exponential form is:

17872 = 2⁴ × 1117¹

Step-3: Factors of 17856

List of positive integer factors of 17856 that divides 17856 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 31, 32, 36, 48, 62, 64, 72, 93, 96, 124, 144, 186, 192, 248, 279, 288, 372, 496, 558, 576, 744, 992, 1116, 1488, 1984, 2232, 2976, 4464, 5952, 8928

Step-4: Factors of 17872

List of positive integer factors of 17872 that divides 17856 without a remainder.

1, 2, 4, 8, 16, 1117, 2234, 4468, 8936

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17856 and 17872. The biggest common factor number is the GCF number.
So the greatest common factor 17856 and 17872 is 16.

Also check out the Least Common Multiple of 17856 and 17872