What are the divisors of 344?

1, 2, 4, 8, 43, 86, 172, 344

There is a total of 8 positive divisors.
The sum of these divisors is 660.
The arithmetic mean is 82.5.

6 even divisors

2, 4, 8, 86, 172, 344

2 odd divisors

1, 43

How to compute the divisors of 344?

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 344 by each of the numbers from 1 to 344 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)

344 / 1 = 344 (the remainder is 0, so 1 is a divisor of 344)
344 / 2 = 172 (the remainder is 0, so 2 is a divisor of 344)
344 / 3 = 114.66666666667 (the remainder is 2, so 3 is not a divisor of 344)
...
344 / 343 = 1.002915451895 (the remainder is 1, so 343 is not a divisor of 344)
344 / 344 = 1 (the remainder is 0, so 344 is a divisor of 344)

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 344 (i.e. 18.547236990991). 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 $\frac{N}{d} = D$ )

344 / 1 = 344 (the remainder is 0, so 1 and 344 are divisors of 344)
344 / 2 = 172 (the remainder is 0, so 2 and 172 are divisors of 344)
344 / 3 = 114.66666666667 (the remainder is 2, so 3 is not a divisor of 344)
...
344 / 17 = 20.235294117647 (the remainder is 4, so 17 is not a divisor of 344)
344 / 18 = 19.111111111111 (the remainder is 2, so 18 is not a divisor of 344)