What are the divisors of 367?

1, 367

There is a total of 2 positive divisors.
The sum of these divisors is 368.
The arithmetic mean is 184.

2 odd divisors

1, 367

How to compute the divisors of 367?

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 367 by each of the numbers from 1 to 367 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)

367 / 1 = 367 (the remainder is 0, so 1 is a divisor of 367)
367 / 2 = 183.5 (the remainder is 1, so 2 is not a divisor of 367)
367 / 3 = 122.33333333333 (the remainder is 1, so 3 is not a divisor of 367)
...
367 / 366 = 1.0027322404372 (the remainder is 1, so 366 is not a divisor of 367)
367 / 367 = 1 (the remainder is 0, so 367 is a divisor of 367)

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 367 (i.e. 19.157244060668). 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 $\frac{N}{d} = D$ )

367 / 1 = 367 (the remainder is 0, so 1 and 367 are divisors of 367)
367 / 2 = 183.5 (the remainder is 1, so 2 is not a divisor of 367)
367 / 3 = 122.33333333333 (the remainder is 1, so 3 is not a divisor of 367)
...
367 / 18 = 20.388888888889 (the remainder is 7, so 18 is not a divisor of 367)
367 / 19 = 19.315789473684 (the remainder is 6, so 19 is not a divisor of 367)