What are the divisors of 359?

1, 359

There is a total of 2 positive divisors.
The sum of these divisors is 360.
The arithmetic mean is 180.

2 odd divisors

1, 359

How to compute the divisors of 359?

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 359 by each of the numbers from 1 to 359 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)

359 / 1 = 359 (the remainder is 0, so 1 is a divisor of 359)
359 / 2 = 179.5 (the remainder is 1, so 2 is not a divisor of 359)
359 / 3 = 119.66666666667 (the remainder is 2, so 3 is not a divisor of 359)
...
359 / 358 = 1.0027932960894 (the remainder is 1, so 358 is not a divisor of 359)
359 / 359 = 1 (the remainder is 0, so 359 is a divisor of 359)

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 359 (i.e. 18.947295321496). 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 $\frac{N}{d} = D$ )

359 / 1 = 359 (the remainder is 0, so 1 and 359 are divisors of 359)
359 / 2 = 179.5 (the remainder is 1, so 2 is not a divisor of 359)
359 / 3 = 119.66666666667 (the remainder is 2, so 3 is not a divisor of 359)
...
359 / 17 = 21.117647058824 (the remainder is 2, so 17 is not a divisor of 359)
359 / 18 = 19.944444444444 (the remainder is 17, so 18 is not a divisor of 359)