What is the Greatest Common Factor of 51584 and 51600?

Greatest common factor (GCF) of 51584 and 51600 is 16.

GCF(51584,51600) = 16

We will now calculate the prime factors of 51584 and 51600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 51584 and 51600.

How to find the GCF of 51584 and 51600?

We will first find the prime factorization of 51584 and 51600. After we will calculate the factors of 51584 and 51600 and find the biggest common factor number .

Step-1: Prime Factorization of 51584

Prime factors of 51584 are 2, 13, 31. Prime factorization of 51584 in exponential form is:

51584 = 2⁷ × 13¹ × 31¹

Step-2: Prime Factorization of 51600

Prime factors of 51600 are 2, 3, 5, 43. Prime factorization of 51600 in exponential form is:

51600 = 2⁴ × 3¹ × 5² × 43¹

Step-3: Factors of 51584

List of positive integer factors of 51584 that divides 51584 without a remainder.

1, 2, 4, 8, 13, 16, 26, 31, 32, 52, 62, 64, 104, 124, 128, 208, 248, 403, 416, 496, 806, 832, 992, 1612, 1664, 1984, 3224, 3968, 6448, 12896, 25792

Step-4: Factors of 51600

List of positive integer factors of 51600 that divides 51584 without a remainder.

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 43, 48, 50, 60, 75, 80, 86, 100, 120, 129, 150, 172, 200, 215, 240, 258, 300, 344, 400, 430, 516, 600, 645, 688, 860, 1032, 1075, 1200, 1290, 1720, 2064, 2150, 2580, 3225, 3440, 4300, 5160, 6450, 8600, 10320, 12900, 17200, 25800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 51584 and 51600. The biggest common factor number is the GCF number.
So the greatest common factor 51584 and 51600 is 16.

Also check out the Least Common Multiple of 51584 and 51600