What are the divisors of 358?

1, 2, 179, 358

There is a total of 4 positive divisors.
The sum of these divisors is 540.
The arithmetic mean is 135.

2 even divisors

2, 358

2 odd divisors

1, 179

How to compute the divisors of 358?

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 358 by each of the numbers from 1 to 358 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)

358 / 1 = 358 (the remainder is 0, so 1 is a divisor of 358)
358 / 2 = 179 (the remainder is 0, so 2 is a divisor of 358)
358 / 3 = 119.33333333333 (the remainder is 1, so 3 is not a divisor of 358)
...
358 / 357 = 1.0028011204482 (the remainder is 1, so 357 is not a divisor of 358)
358 / 358 = 1 (the remainder is 0, so 358 is a divisor of 358)

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 358 (i.e. 18.920887928425). 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 $\frac{N}{d} = D$ )

358 / 1 = 358 (the remainder is 0, so 1 and 358 are divisors of 358)
358 / 2 = 179 (the remainder is 0, so 2 and 179 are divisors of 358)
358 / 3 = 119.33333333333 (the remainder is 1, so 3 is not a divisor of 358)
...
358 / 17 = 21.058823529412 (the remainder is 1, so 17 is not a divisor of 358)
358 / 18 = 19.888888888889 (the remainder is 16, so 18 is not a divisor of 358)