What are the divisors of 2803?

1, 2803

There is a total of 2 positive divisors.
The sum of these divisors is 2804.
The arithmetic mean is 1402.

2 odd divisors

1, 2803

How to compute the divisors of 2803?

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 2803 by each of the numbers from 1 to 2803 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)

2803 / 1 = 2803 (the remainder is 0, so 1 is a divisor of 2803)
2803 / 2 = 1401.5 (the remainder is 1, so 2 is not a divisor of 2803)
2803 / 3 = 934.33333333333 (the remainder is 1, so 3 is not a divisor of 2803)
...
2803 / 2802 = 1.0003568879372 (the remainder is 1, so 2802 is not a divisor of 2803)
2803 / 2803 = 1 (the remainder is 0, so 2803 is a divisor of 2803)

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 2803 (i.e. 52.943365967796). 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 $\frac{N}{d} = D$ )

2803 / 1 = 2803 (the remainder is 0, so 1 and 2803 are divisors of 2803)
2803 / 2 = 1401.5 (the remainder is 1, so 2 is not a divisor of 2803)
2803 / 3 = 934.33333333333 (the remainder is 1, so 3 is not a divisor of 2803)
...
2803 / 51 = 54.960784313725 (the remainder is 49, so 51 is not a divisor of 2803)
2803 / 52 = 53.903846153846 (the remainder is 47, so 52 is not a divisor of 2803)