What are the divisors of 3489?

1, 3, 1163, 3489

There is a total of 4 positive divisors.
The sum of these divisors is 4656.
The arithmetic mean is 1164.

4 odd divisors

1, 3, 1163, 3489

How to compute the divisors of 3489?

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 3489 by each of the numbers from 1 to 3489 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)

3489 / 1 = 3489 (the remainder is 0, so 1 is a divisor of 3489)
3489 / 2 = 1744.5 (the remainder is 1, so 2 is not a divisor of 3489)
3489 / 3 = 1163 (the remainder is 0, so 3 is a divisor of 3489)
...
3489 / 3488 = 1.0002866972477 (the remainder is 1, so 3488 is not a divisor of 3489)
3489 / 3489 = 1 (the remainder is 0, so 3489 is a divisor of 3489)

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 3489 (i.e. 59.067757702489). 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 $\frac{N}{d} = D$ )

3489 / 1 = 3489 (the remainder is 0, so 1 and 3489 are divisors of 3489)
3489 / 2 = 1744.5 (the remainder is 1, so 2 is not a divisor of 3489)
3489 / 3 = 1163 (the remainder is 0, so 3 and 1163 are divisors of 3489)
...
3489 / 58 = 60.155172413793 (the remainder is 9, so 58 is not a divisor of 3489)
3489 / 59 = 59.135593220339 (the remainder is 8, so 59 is not a divisor of 3489)