What is the Greatest Common Factor of 53584 and 53600?

Greatest common factor (GCF) of 53584 and 53600 is 16.

GCF(53584,53600) = 16

We will now calculate the prime factors of 53584 and 53600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 53584 and 53600.

How to find the GCF of 53584 and 53600?

We will first find the prime factorization of 53584 and 53600. After we will calculate the factors of 53584 and 53600 and find the biggest common factor number .

Step-1: Prime Factorization of 53584

Prime factors of 53584 are 2, 17, 197. Prime factorization of 53584 in exponential form is:

53584 = 2⁴ × 17¹ × 197¹

Step-2: Prime Factorization of 53600

Prime factors of 53600 are 2, 5, 67. Prime factorization of 53600 in exponential form is:

53600 = 2⁵ × 5² × 67¹

Step-3: Factors of 53584

List of positive integer factors of 53584 that divides 53584 without a remainder.

1, 2, 4, 8, 16, 17, 34, 68, 136, 197, 272, 394, 788, 1576, 3152, 3349, 6698, 13396, 26792

Step-4: Factors of 53600

List of positive integer factors of 53600 that divides 53584 without a remainder.

1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 67, 80, 100, 134, 160, 200, 268, 335, 400, 536, 670, 800, 1072, 1340, 1675, 2144, 2680, 3350, 5360, 6700, 10720, 13400, 26800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 53584 and 53600. The biggest common factor number is the GCF number.
So the greatest common factor 53584 and 53600 is 16.

Also check out the Least Common Multiple of 53584 and 53600