What are the divisors of 3459?

1, 3, 1153, 3459

There is a total of 4 positive divisors.
The sum of these divisors is 4616.
The arithmetic mean is 1154.

4 odd divisors

1, 3, 1153, 3459

How to compute the divisors of 3459?

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 3459 by each of the numbers from 1 to 3459 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)

3459 / 1 = 3459 (the remainder is 0, so 1 is a divisor of 3459)
3459 / 2 = 1729.5 (the remainder is 1, so 2 is not a divisor of 3459)
3459 / 3 = 1153 (the remainder is 0, so 3 is a divisor of 3459)
...
3459 / 3458 = 1.0002891844997 (the remainder is 1, so 3458 is not a divisor of 3459)
3459 / 3459 = 1 (the remainder is 0, so 3459 is a divisor of 3459)

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 3459 (i.e. 58.81326381013). 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 $\frac{N}{d} = D$ )

3459 / 1 = 3459 (the remainder is 0, so 1 and 3459 are divisors of 3459)
3459 / 2 = 1729.5 (the remainder is 1, so 2 is not a divisor of 3459)
3459 / 3 = 1153 (the remainder is 0, so 3 and 1153 are divisors of 3459)
...
3459 / 57 = 60.684210526316 (the remainder is 39, so 57 is not a divisor of 3459)
3459 / 58 = 59.637931034483 (the remainder is 37, so 58 is not a divisor of 3459)