What are the divisors of 5404?

1, 2, 4, 7, 14, 28, 193, 386, 772, 1351, 2702, 5404

There is a total of 12 positive divisors.
The sum of these divisors is 10864.
The arithmetic mean is 905.33333333333.

8 even divisors

2, 4, 14, 28, 386, 772, 2702, 5404

4 odd divisors

1, 7, 193, 1351

How to compute the divisors of 5404?

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 5404 by each of the numbers from 1 to 5404 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)

5404 / 1 = 5404 (the remainder is 0, so 1 is a divisor of 5404)
5404 / 2 = 2702 (the remainder is 0, so 2 is a divisor of 5404)
5404 / 3 = 1801.3333333333 (the remainder is 1, so 3 is not a divisor of 5404)
...
5404 / 5403 = 1.0001850823617 (the remainder is 1, so 5403 is not a divisor of 5404)
5404 / 5404 = 1 (the remainder is 0, so 5404 is a divisor of 5404)

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 5404 (i.e. 73.511903797956). 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 $\frac{N}{d} = D$ )

5404 / 1 = 5404 (the remainder is 0, so 1 and 5404 are divisors of 5404)
5404 / 2 = 2702 (the remainder is 0, so 2 and 2702 are divisors of 5404)
5404 / 3 = 1801.3333333333 (the remainder is 1, so 3 is not a divisor of 5404)
...
5404 / 72 = 75.055555555556 (the remainder is 4, so 72 is not a divisor of 5404)
5404 / 73 = 74.027397260274 (the remainder is 2, so 73 is not a divisor of 5404)