What are the divisors of 3416?

1, 2, 4, 7, 8, 14, 28, 56, 61, 122, 244, 427, 488, 854, 1708, 3416

There is a total of 16 positive divisors.
The sum of these divisors is 7440.
The arithmetic mean is 465.

12 even divisors

2, 4, 8, 14, 28, 56, 122, 244, 488, 854, 1708, 3416

4 odd divisors

1, 7, 61, 427

How to compute the divisors of 3416?

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 3416 by each of the numbers from 1 to 3416 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)

3416 / 1 = 3416 (the remainder is 0, so 1 is a divisor of 3416)
3416 / 2 = 1708 (the remainder is 0, so 2 is a divisor of 3416)
3416 / 3 = 1138.6666666667 (the remainder is 2, so 3 is not a divisor of 3416)
...
3416 / 3415 = 1.0002928257687 (the remainder is 1, so 3415 is not a divisor of 3416)
3416 / 3416 = 1 (the remainder is 0, so 3416 is a divisor of 3416)

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 3416 (i.e. 58.44655678481). 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 $\frac{N}{d} = D$ )

3416 / 1 = 3416 (the remainder is 0, so 1 and 3416 are divisors of 3416)
3416 / 2 = 1708 (the remainder is 0, so 2 and 1708 are divisors of 3416)
3416 / 3 = 1138.6666666667 (the remainder is 2, so 3 is not a divisor of 3416)
...
3416 / 57 = 59.929824561404 (the remainder is 53, so 57 is not a divisor of 3416)
3416 / 58 = 58.896551724138 (the remainder is 52, so 58 is not a divisor of 3416)