What are the divisors of 3468?

1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204, 289, 578, 867, 1156, 1734, 3468

There is a total of 18 positive divisors.
The sum of these divisors is 8596.
The arithmetic mean is 477.55555555556.

12 even divisors

2, 4, 6, 12, 34, 68, 102, 204, 578, 1156, 1734, 3468

6 odd divisors

1, 3, 17, 51, 289, 867

How to compute the divisors of 3468?

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 3468 by each of the numbers from 1 to 3468 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)

3468 / 1 = 3468 (the remainder is 0, so 1 is a divisor of 3468)
3468 / 2 = 1734 (the remainder is 0, so 2 is a divisor of 3468)
3468 / 3 = 1156 (the remainder is 0, so 3 is a divisor of 3468)
...
3468 / 3467 = 1.0002884338044 (the remainder is 1, so 3467 is not a divisor of 3468)
3468 / 3468 = 1 (the remainder is 0, so 3468 is a divisor of 3468)

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 3468 (i.e. 58.889727457342). 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 $\frac{N}{d} = D$ )

3468 / 1 = 3468 (the remainder is 0, so 1 and 3468 are divisors of 3468)
3468 / 2 = 1734 (the remainder is 0, so 2 and 1734 are divisors of 3468)
3468 / 3 = 1156 (the remainder is 0, so 3 and 1156 are divisors of 3468)
...
3468 / 57 = 60.842105263158 (the remainder is 48, so 57 is not a divisor of 3468)
3468 / 58 = 59.793103448276 (the remainder is 46, so 58 is not a divisor of 3468)