What are the divisors of 366?

1, 2, 3, 6, 61, 122, 183, 366

There is a total of 8 positive divisors.
The sum of these divisors is 744.
The arithmetic mean is 93.

4 even divisors

2, 6, 122, 366

4 odd divisors

1, 3, 61, 183

How to compute the divisors of 366?

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 366 by each of the numbers from 1 to 366 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)

366 / 1 = 366 (the remainder is 0, so 1 is a divisor of 366)
366 / 2 = 183 (the remainder is 0, so 2 is a divisor of 366)
366 / 3 = 122 (the remainder is 0, so 3 is a divisor of 366)
...
366 / 365 = 1.0027397260274 (the remainder is 1, so 365 is not a divisor of 366)
366 / 366 = 1 (the remainder is 0, so 366 is a divisor of 366)

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 366 (i.e. 19.131126469709). 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 $\frac{N}{d} = D$ )

366 / 1 = 366 (the remainder is 0, so 1 and 366 are divisors of 366)
366 / 2 = 183 (the remainder is 0, so 2 and 183 are divisors of 366)
366 / 3 = 122 (the remainder is 0, so 3 and 122 are divisors of 366)
...
366 / 18 = 20.333333333333 (the remainder is 6, so 18 is not a divisor of 366)
366 / 19 = 19.263157894737 (the remainder is 5, so 19 is not a divisor of 366)