What are the divisors of 5503?

1, 5503

There is a total of 2 positive divisors.
The sum of these divisors is 5504.
The arithmetic mean is 2752.

2 odd divisors

1, 5503

How to compute the divisors of 5503?

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 5503 by each of the numbers from 1 to 5503 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)

5503 / 1 = 5503 (the remainder is 0, so 1 is a divisor of 5503)
5503 / 2 = 2751.5 (the remainder is 1, so 2 is not a divisor of 5503)
5503 / 3 = 1834.3333333333 (the remainder is 1, so 3 is not a divisor of 5503)
...
5503 / 5502 = 1.0001817520901 (the remainder is 1, so 5502 is not a divisor of 5503)
5503 / 5503 = 1 (the remainder is 0, so 5503 is a divisor of 5503)

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 5503 (i.e. 74.182208109492). 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 $\frac{N}{d} = D$ )

5503 / 1 = 5503 (the remainder is 0, so 1 and 5503 are divisors of 5503)
5503 / 2 = 2751.5 (the remainder is 1, so 2 is not a divisor of 5503)
5503 / 3 = 1834.3333333333 (the remainder is 1, so 3 is not a divisor of 5503)
...
5503 / 73 = 75.383561643836 (the remainder is 28, so 73 is not a divisor of 5503)
5503 / 74 = 74.364864864865 (the remainder is 27, so 74 is not a divisor of 5503)