What are the divisors of 3411?

1, 3, 9, 379, 1137, 3411

There is a total of 6 positive divisors.
The sum of these divisors is 4940.
The arithmetic mean is 823.33333333333.

6 odd divisors

1, 3, 9, 379, 1137, 3411

How to compute the divisors of 3411?

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 3411 by each of the numbers from 1 to 3411 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)

3411 / 1 = 3411 (the remainder is 0, so 1 is a divisor of 3411)
3411 / 2 = 1705.5 (the remainder is 1, so 2 is not a divisor of 3411)
3411 / 3 = 1137 (the remainder is 0, so 3 is a divisor of 3411)
...
3411 / 3410 = 1.000293255132 (the remainder is 1, so 3410 is not a divisor of 3411)
3411 / 3411 = 1 (the remainder is 0, so 3411 is a divisor of 3411)

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 3411 (i.e. 58.403767001795). 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 $\frac{N}{d} = D$ )

3411 / 1 = 3411 (the remainder is 0, so 1 and 3411 are divisors of 3411)
3411 / 2 = 1705.5 (the remainder is 1, so 2 is not a divisor of 3411)
3411 / 3 = 1137 (the remainder is 0, so 3 and 1137 are divisors of 3411)
...
3411 / 57 = 59.842105263158 (the remainder is 48, so 57 is not a divisor of 3411)
3411 / 58 = 58.810344827586 (the remainder is 47, so 58 is not a divisor of 3411)