What are the divisors of 3422?

1, 2, 29, 58, 59, 118, 1711, 3422

There is a total of 8 positive divisors.
The sum of these divisors is 5400.
The arithmetic mean is 675.

4 even divisors

2, 58, 118, 3422

4 odd divisors

1, 29, 59, 1711

How to compute the divisors of 3422?

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 3422 by each of the numbers from 1 to 3422 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)

3422 / 1 = 3422 (the remainder is 0, so 1 is a divisor of 3422)
3422 / 2 = 1711 (the remainder is 0, so 2 is a divisor of 3422)
3422 / 3 = 1140.6666666667 (the remainder is 2, so 3 is not a divisor of 3422)
...
3422 / 3421 = 1.0002923121894 (the remainder is 1, so 3421 is not a divisor of 3422)
3422 / 3422 = 1 (the remainder is 0, so 3422 is a divisor of 3422)

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 3422 (i.e. 58.497863208839). 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 $\frac{N}{d} = D$ )

3422 / 1 = 3422 (the remainder is 0, so 1 and 3422 are divisors of 3422)
3422 / 2 = 1711 (the remainder is 0, so 2 and 1711 are divisors of 3422)
3422 / 3 = 1140.6666666667 (the remainder is 2, so 3 is not a divisor of 3422)
...
3422 / 57 = 60.035087719298 (the remainder is 2, so 57 is not a divisor of 3422)
3422 / 58 = 59 (the remainder is 0, so 58 and 59 are divisors of 3422)