What are the divisors of 349?

1, 349

There is a total of 2 positive divisors.
The sum of these divisors is 350.
The arithmetic mean is 175.

2 odd divisors

1, 349

How to compute the divisors of 349?

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 349 by each of the numbers from 1 to 349 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)

349 / 1 = 349 (the remainder is 0, so 1 is a divisor of 349)
349 / 2 = 174.5 (the remainder is 1, so 2 is not a divisor of 349)
349 / 3 = 116.33333333333 (the remainder is 1, so 3 is not a divisor of 349)
...
349 / 348 = 1.0028735632184 (the remainder is 1, so 348 is not a divisor of 349)
349 / 349 = 1 (the remainder is 0, so 349 is a divisor of 349)

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 349 (i.e. 18.681541692269). 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 $\frac{N}{d} = D$ )

349 / 1 = 349 (the remainder is 0, so 1 and 349 are divisors of 349)
349 / 2 = 174.5 (the remainder is 1, so 2 is not a divisor of 349)
349 / 3 = 116.33333333333 (the remainder is 1, so 3 is not a divisor of 349)
...
349 / 17 = 20.529411764706 (the remainder is 9, so 17 is not a divisor of 349)
349 / 18 = 19.388888888889 (the remainder is 7, so 18 is not a divisor of 349)