What are the divisors of 355?

1, 5, 71, 355

There is a total of 4 positive divisors.
The sum of these divisors is 432.
The arithmetic mean is 108.

4 odd divisors

1, 5, 71, 355

How to compute the divisors of 355?

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 355 by each of the numbers from 1 to 355 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)

355 / 1 = 355 (the remainder is 0, so 1 is a divisor of 355)
355 / 2 = 177.5 (the remainder is 1, so 2 is not a divisor of 355)
355 / 3 = 118.33333333333 (the remainder is 1, so 3 is not a divisor of 355)
...
355 / 354 = 1.0028248587571 (the remainder is 1, so 354 is not a divisor of 355)
355 / 355 = 1 (the remainder is 0, so 355 is a divisor of 355)

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 355 (i.e. 18.841443681417). 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 $\frac{N}{d} = D$ )

355 / 1 = 355 (the remainder is 0, so 1 and 355 are divisors of 355)
355 / 2 = 177.5 (the remainder is 1, so 2 is not a divisor of 355)
355 / 3 = 118.33333333333 (the remainder is 1, so 3 is not a divisor of 355)
...
355 / 17 = 20.882352941176 (the remainder is 15, so 17 is not a divisor of 355)
355 / 18 = 19.722222222222 (the remainder is 13, so 18 is not a divisor of 355)