What are the divisors of 5603?

1, 13, 431, 5603

There is a total of 4 positive divisors.
The sum of these divisors is 6048.
The arithmetic mean is 1512.

4 odd divisors

1, 13, 431, 5603

How to compute the divisors of 5603?

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 5603 by each of the numbers from 1 to 5603 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)

5603 / 1 = 5603 (the remainder is 0, so 1 is a divisor of 5603)
5603 / 2 = 2801.5 (the remainder is 1, so 2 is not a divisor of 5603)
5603 / 3 = 1867.6666666667 (the remainder is 2, so 3 is not a divisor of 5603)
...
5603 / 5602 = 1.0001785076758 (the remainder is 1, so 5602 is not a divisor of 5603)
5603 / 5603 = 1 (the remainder is 0, so 5603 is a divisor of 5603)

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 5603 (i.e. 74.853189644797). 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 $\frac{N}{d} = D$ )

5603 / 1 = 5603 (the remainder is 0, so 1 and 5603 are divisors of 5603)
5603 / 2 = 2801.5 (the remainder is 1, so 2 is not a divisor of 5603)
5603 / 3 = 1867.6666666667 (the remainder is 2, so 3 is not a divisor of 5603)
...
5603 / 73 = 76.753424657534 (the remainder is 55, so 73 is not a divisor of 5603)
5603 / 74 = 75.716216216216 (the remainder is 53, so 74 is not a divisor of 5603)