What are the divisors of 3918?

1, 2, 3, 6, 653, 1306, 1959, 3918

There is a total of 8 positive divisors.
The sum of these divisors is 7848.
The arithmetic mean is 981.

4 even divisors

2, 6, 1306, 3918

4 odd divisors

1, 3, 653, 1959

How to compute the divisors of 3918?

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 3918 by each of the numbers from 1 to 3918 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)

3918 / 1 = 3918 (the remainder is 0, so 1 is a divisor of 3918)
3918 / 2 = 1959 (the remainder is 0, so 2 is a divisor of 3918)
3918 / 3 = 1306 (the remainder is 0, so 3 is a divisor of 3918)
...
3918 / 3917 = 1.0002552974215 (the remainder is 1, so 3917 is not a divisor of 3918)
3918 / 3918 = 1 (the remainder is 0, so 3918 is a divisor of 3918)

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 3918 (i.e. 62.593929418115). 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 $\frac{N}{d} = D$ )

3918 / 1 = 3918 (the remainder is 0, so 1 and 3918 are divisors of 3918)
3918 / 2 = 1959 (the remainder is 0, so 2 and 1959 are divisors of 3918)
3918 / 3 = 1306 (the remainder is 0, so 3 and 1306 are divisors of 3918)
...
3918 / 61 = 64.229508196721 (the remainder is 14, so 61 is not a divisor of 3918)
3918 / 62 = 63.193548387097 (the remainder is 12, so 62 is not a divisor of 3918)