What is the Greatest Common Factor of 17584 and 17600?

Greatest common factor (GCF) of 17584 and 17600 is 16.

GCF(17584,17600) = 16

We will now calculate the prime factors of 17584 and 17600, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 17584 and 17600.

How to find the GCF of 17584 and 17600?

We will first find the prime factorization of 17584 and 17600. After we will calculate the factors of 17584 and 17600 and find the biggest common factor number .

Step-1: Prime Factorization of 17584

Prime factors of 17584 are 2, 7, 157. Prime factorization of 17584 in exponential form is:

17584 = 2⁴ × 7¹ × 157¹

Step-2: Prime Factorization of 17600

Prime factors of 17600 are 2, 5, 11. Prime factorization of 17600 in exponential form is:

17600 = 2⁶ × 5² × 11¹

Step-3: Factors of 17584

List of positive integer factors of 17584 that divides 17584 without a remainder.

1, 2, 4, 7, 8, 14, 16, 28, 56, 112, 157, 314, 628, 1099, 1256, 2198, 2512, 4396, 8792

Step-4: Factors of 17600

List of positive integer factors of 17600 that divides 17584 without a remainder.

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 25, 32, 40, 44, 50, 55, 64, 80, 88, 100, 110, 160, 176, 200, 220, 275, 320, 352, 400, 440, 550, 704, 800, 880, 1100, 1600, 1760, 2200, 3520, 4400, 8800

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 17584 and 17600. The biggest common factor number is the GCF number.
So the greatest common factor 17584 and 17600 is 16.

Also check out the Least Common Multiple of 17584 and 17600