What are the divisors of 346?

1, 2, 173, 346

There is a total of 4 positive divisors.
The sum of these divisors is 522.
The arithmetic mean is 130.5.

2 even divisors

2, 346

2 odd divisors

1, 173

How to compute the divisors of 346?

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 346 by each of the numbers from 1 to 346 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)

346 / 1 = 346 (the remainder is 0, so 1 is a divisor of 346)
346 / 2 = 173 (the remainder is 0, so 2 is a divisor of 346)
346 / 3 = 115.33333333333 (the remainder is 1, so 3 is not a divisor of 346)
...
346 / 345 = 1.0028985507246 (the remainder is 1, so 345 is not a divisor of 346)
346 / 346 = 1 (the remainder is 0, so 346 is a divisor of 346)

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 346 (i.e. 18.601075237738). 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 $\frac{N}{d} = D$ )

346 / 1 = 346 (the remainder is 0, so 1 and 346 are divisors of 346)
346 / 2 = 173 (the remainder is 0, so 2 and 173 are divisors of 346)
346 / 3 = 115.33333333333 (the remainder is 1, so 3 is not a divisor of 346)
...
346 / 17 = 20.352941176471 (the remainder is 6, so 17 is not a divisor of 346)
346 / 18 = 19.222222222222 (the remainder is 4, so 18 is not a divisor of 346)