What are the divisors of 184?

1, 2, 4, 8, 23, 46, 92, 184

There is a total of 8 positive divisors.
The sum of these divisors is 360.
The arithmetic mean is 45.

6 even divisors

2, 4, 8, 46, 92, 184

2 odd divisors

1, 23

How to compute the divisors of 184?

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 184 by each of the numbers from 1 to 184 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)

184 / 1 = 184 (the remainder is 0, so 1 is a divisor of 184)
184 / 2 = 92 (the remainder is 0, so 2 is a divisor of 184)
184 / 3 = 61.333333333333 (the remainder is 1, so 3 is not a divisor of 184)
...
184 / 183 = 1.0054644808743 (the remainder is 1, so 183 is not a divisor of 184)
184 / 184 = 1 (the remainder is 0, so 184 is a divisor of 184)

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 184 (i.e. 13.564659966251). 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 $\frac{N}{d} = D$ )

184 / 1 = 184 (the remainder is 0, so 1 and 184 are divisors of 184)
184 / 2 = 92 (the remainder is 0, so 2 and 92 are divisors of 184)
184 / 3 = 61.333333333333 (the remainder is 1, so 3 is not a divisor of 184)
...
184 / 12 = 15.333333333333 (the remainder is 4, so 12 is not a divisor of 184)
184 / 13 = 14.153846153846 (the remainder is 2, so 13 is not a divisor of 184)