What are the divisors of 183?

1, 3, 61, 183

There is a total of 4 positive divisors.
The sum of these divisors is 248.
The arithmetic mean is 62.

4 odd divisors

1, 3, 61, 183

How to compute the divisors of 183?

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 183 by each of the numbers from 1 to 183 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)

183 / 1 = 183 (the remainder is 0, so 1 is a divisor of 183)
183 / 2 = 91.5 (the remainder is 1, so 2 is not a divisor of 183)
183 / 3 = 61 (the remainder is 0, so 3 is a divisor of 183)
...
183 / 182 = 1.0054945054945 (the remainder is 1, so 182 is not a divisor of 183)
183 / 183 = 1 (the remainder is 0, so 183 is a divisor of 183)

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 183 (i.e. 13.527749258469). 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 $\frac{N}{d} = D$ )

183 / 1 = 183 (the remainder is 0, so 1 and 183 are divisors of 183)
183 / 2 = 91.5 (the remainder is 1, so 2 is not a divisor of 183)
183 / 3 = 61 (the remainder is 0, so 3 and 61 are divisors of 183)
...
183 / 12 = 15.25 (the remainder is 3, so 12 is not a divisor of 183)
183 / 13 = 14.076923076923 (the remainder is 1, so 13 is not a divisor of 183)