What are the divisors of 3418?

1, 2, 1709, 3418

There is a total of 4 positive divisors.
The sum of these divisors is 5130.
The arithmetic mean is 1282.5.

2 even divisors

2, 3418

2 odd divisors

1, 1709

How to compute the divisors of 3418?

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 3418 by each of the numbers from 1 to 3418 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)

3418 / 1 = 3418 (the remainder is 0, so 1 is a divisor of 3418)
3418 / 2 = 1709 (the remainder is 0, so 2 is a divisor of 3418)
3418 / 3 = 1139.3333333333 (the remainder is 1, so 3 is not a divisor of 3418)
...
3418 / 3417 = 1.0002926543752 (the remainder is 1, so 3417 is not a divisor of 3418)
3418 / 3418 = 1 (the remainder is 0, so 3418 is a divisor of 3418)

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 3418 (i.e. 58.463663928974). 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 $\frac{N}{d} = D$ )

3418 / 1 = 3418 (the remainder is 0, so 1 and 3418 are divisors of 3418)
3418 / 2 = 1709 (the remainder is 0, so 2 and 1709 are divisors of 3418)
3418 / 3 = 1139.3333333333 (the remainder is 1, so 3 is not a divisor of 3418)
...
3418 / 57 = 59.964912280702 (the remainder is 55, so 57 is not a divisor of 3418)
3418 / 58 = 58.931034482759 (the remainder is 54, so 58 is not a divisor of 3418)