What are the divisors of 3359?

1, 3359

There is a total of 2 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 1680.

2 odd divisors

1, 3359

How to compute the divisors of 3359?

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 3359 by each of the numbers from 1 to 3359 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)

3359 / 1 = 3359 (the remainder is 0, so 1 is a divisor of 3359)
3359 / 2 = 1679.5 (the remainder is 1, so 2 is not a divisor of 3359)
3359 / 3 = 1119.6666666667 (the remainder is 2, so 3 is not a divisor of 3359)
...
3359 / 3358 = 1.0002977963073 (the remainder is 1, so 3358 is not a divisor of 3359)
3359 / 3359 = 1 (the remainder is 0, so 3359 is a divisor of 3359)

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 3359 (i.e. 57.956880523368). 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 $\frac{N}{d} = D$ )

3359 / 1 = 3359 (the remainder is 0, so 1 and 3359 are divisors of 3359)
3359 / 2 = 1679.5 (the remainder is 1, so 2 is not a divisor of 3359)
3359 / 3 = 1119.6666666667 (the remainder is 2, so 3 is not a divisor of 3359)
...
3359 / 56 = 59.982142857143 (the remainder is 55, so 56 is not a divisor of 3359)
3359 / 57 = 58.929824561404 (the remainder is 53, so 57 is not a divisor of 3359)