What are the divisors of 3474?

1, 2, 3, 6, 9, 18, 193, 386, 579, 1158, 1737, 3474

There is a total of 12 positive divisors.
The sum of these divisors is 7566.
The arithmetic mean is 630.5.

6 even divisors

2, 6, 18, 386, 1158, 3474

6 odd divisors

1, 3, 9, 193, 579, 1737

How to compute the divisors of 3474?

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 3474 by each of the numbers from 1 to 3474 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)

3474 / 1 = 3474 (the remainder is 0, so 1 is a divisor of 3474)
3474 / 2 = 1737 (the remainder is 0, so 2 is a divisor of 3474)
3474 / 3 = 1158 (the remainder is 0, so 3 is a divisor of 3474)
...
3474 / 3473 = 1.0002879355024 (the remainder is 1, so 3473 is not a divisor of 3474)
3474 / 3474 = 1 (the remainder is 0, so 3474 is a divisor of 3474)

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 3474 (i.e. 58.940648113166). 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 $\frac{N}{d} = D$ )

3474 / 1 = 3474 (the remainder is 0, so 1 and 3474 are divisors of 3474)
3474 / 2 = 1737 (the remainder is 0, so 2 and 1737 are divisors of 3474)
3474 / 3 = 1158 (the remainder is 0, so 3 and 1158 are divisors of 3474)
...
3474 / 57 = 60.947368421053 (the remainder is 54, so 57 is not a divisor of 3474)
3474 / 58 = 59.896551724138 (the remainder is 52, so 58 is not a divisor of 3474)