What is the Greatest Common Factor of 17856 and 17874?

Greatest common factor (GCF) of 17856 and 17874 is 18.

GCF(17856,17874) = 18

We will now calculate the prime factors of 17856 and 17874, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17856 and 17874.

How to find the GCF of 17856 and 17874?

We will first find the prime factorization of 17856 and 17874. After we will calculate the factors of 17856 and 17874 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 17874

Prime factors of 17874 are 2, 3, 331. Prime factorization of 17874 in exponential form is:

17874 = 2¹ × 3³ × 331¹

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 17874

List of positive integer factors of 17874 that divides 17856 without a remainder.

1, 2, 3, 6, 9, 18, 27, 54, 331, 662, 993, 1986, 2979, 5958, 8937

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17856 and 17874. The biggest common factor number is the GCF number.
So the greatest common factor 17856 and 17874 is 18.

Also check out the Least Common Multiple of 17856 and 17874