What are the divisors of 5504?

1, 2, 4, 8, 16, 32, 43, 64, 86, 128, 172, 344, 688, 1376, 2752, 5504

There is a total of 16 positive divisors.
The sum of these divisors is 11220.
The arithmetic mean is 701.25.

14 even divisors

2, 4, 8, 16, 32, 64, 86, 128, 172, 344, 688, 1376, 2752, 5504

2 odd divisors

1, 43

How to compute the divisors of 5504?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 5504 by each of the numbers from 1 to 5504 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

5504 / 1 = 5504 (the remainder is 0, so 1 is a divisor of 5504)
5504 / 2 = 2752 (the remainder is 0, so 2 is a divisor of 5504)
5504 / 3 = 1834.6666666667 (the remainder is 2, so 3 is not a divisor of 5504)
...
5504 / 5503 = 1.0001817190623 (the remainder is 1, so 5503 is not a divisor of 5504)
5504 / 5504 = 1 (the remainder is 0, so 5504 is a divisor of 5504)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 5504 (i.e. 74.188947963966). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

5504 / 1 = 5504 (the remainder is 0, so 1 and 5504 are divisors of 5504)
5504 / 2 = 2752 (the remainder is 0, so 2 and 2752 are divisors of 5504)
5504 / 3 = 1834.6666666667 (the remainder is 2, so 3 is not a divisor of 5504)
...
5504 / 73 = 75.397260273973 (the remainder is 29, so 73 is not a divisor of 5504)
5504 / 74 = 74.378378378378 (the remainder is 28, so 74 is not a divisor of 5504)