What are the divisors of 2183?

1, 37, 59, 2183

There is a total of 4 positive divisors.
The sum of these divisors is 2280.
The arithmetic mean is 570.

4 odd divisors

1, 37, 59, 2183

How to compute the divisors of 2183?

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 2183 by each of the numbers from 1 to 2183 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)

2183 / 1 = 2183 (the remainder is 0, so 1 is a divisor of 2183)
2183 / 2 = 1091.5 (the remainder is 1, so 2 is not a divisor of 2183)
2183 / 3 = 727.66666666667 (the remainder is 2, so 3 is not a divisor of 2183)
...
2183 / 2182 = 1.0004582951421 (the remainder is 1, so 2182 is not a divisor of 2183)
2183 / 2183 = 1 (the remainder is 0, so 2183 is a divisor of 2183)

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 2183 (i.e. 46.722585544895). 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 $\frac{N}{d} = D$ )

2183 / 1 = 2183 (the remainder is 0, so 1 and 2183 are divisors of 2183)
2183 / 2 = 1091.5 (the remainder is 1, so 2 is not a divisor of 2183)
2183 / 3 = 727.66666666667 (the remainder is 2, so 3 is not a divisor of 2183)
...
2183 / 45 = 48.511111111111 (the remainder is 23, so 45 is not a divisor of 2183)
2183 / 46 = 47.45652173913 (the remainder is 21, so 46 is not a divisor of 2183)