What are the divisors of 356?

1, 2, 4, 89, 178, 356

There is a total of 6 positive divisors.
The sum of these divisors is 630.
The arithmetic mean is 105.

4 even divisors

2, 4, 178, 356

2 odd divisors

1, 89

How to compute the divisors of 356?

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 356 by each of the numbers from 1 to 356 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)

356 / 1 = 356 (the remainder is 0, so 1 is a divisor of 356)
356 / 2 = 178 (the remainder is 0, so 2 is a divisor of 356)
356 / 3 = 118.66666666667 (the remainder is 2, so 3 is not a divisor of 356)
...
356 / 355 = 1.0028169014085 (the remainder is 1, so 355 is not a divisor of 356)
356 / 356 = 1 (the remainder is 0, so 356 is a divisor of 356)

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 356 (i.e. 18.867962264113). 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 $\frac{N}{d} = D$ )

356 / 1 = 356 (the remainder is 0, so 1 and 356 are divisors of 356)
356 / 2 = 178 (the remainder is 0, so 2 and 178 are divisors of 356)
356 / 3 = 118.66666666667 (the remainder is 2, so 3 is not a divisor of 356)
...
356 / 17 = 20.941176470588 (the remainder is 16, so 17 is not a divisor of 356)
356 / 18 = 19.777777777778 (the remainder is 14, so 18 is not a divisor of 356)