What is the Greatest Common Factor of 41584 and 41600?

Greatest common factor (GCF) of 41584 and 41600 is 16.

GCF(41584,41600) = 16

We will now calculate the prime factors of 41584 and 41600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 41584 and 41600.

How to find the GCF of 41584 and 41600?

We will first find the prime factorization of 41584 and 41600. After we will calculate the factors of 41584 and 41600 and find the biggest common factor number .

Step-1: Prime Factorization of 41584

Prime factors of 41584 are 2, 23, 113. Prime factorization of 41584 in exponential form is:

41584 = 2⁴ × 23¹ × 113¹

Step-2: Prime Factorization of 41600

Prime factors of 41600 are 2, 5, 13. Prime factorization of 41600 in exponential form is:

41600 = 2⁷ × 5² × 13¹

Step-3: Factors of 41584

List of positive integer factors of 41584 that divides 41584 without a remainder.

1, 2, 4, 8, 16, 23, 46, 92, 113, 184, 226, 368, 452, 904, 1808, 2599, 5198, 10396, 20792

Step-4: Factors of 41600

List of positive integer factors of 41600 that divides 41584 without a remainder.

1, 2, 4, 5, 8, 10, 13, 16, 20, 25, 26, 32, 40, 50, 52, 64, 65, 80, 100, 104, 128, 130, 160, 200, 208, 260, 320, 325, 400, 416, 520, 640, 650, 800, 832, 1040, 1300, 1600, 1664, 2080, 2600, 3200, 4160, 5200, 8320, 10400, 20800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 41584 and 41600. The biggest common factor number is the GCF number.
So the greatest common factor 41584 and 41600 is 16.

Also check out the Least Common Multiple of 41584 and 41600