What are the divisors of 3916?

1, 2, 4, 11, 22, 44, 89, 178, 356, 979, 1958, 3916

There is a total of 12 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 630.

8 even divisors

2, 4, 22, 44, 178, 356, 1958, 3916

4 odd divisors

1, 11, 89, 979

How to compute the divisors of 3916?

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 3916 by each of the numbers from 1 to 3916 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)

3916 / 1 = 3916 (the remainder is 0, so 1 is a divisor of 3916)
3916 / 2 = 1958 (the remainder is 0, so 2 is a divisor of 3916)
3916 / 3 = 1305.3333333333 (the remainder is 1, so 3 is not a divisor of 3916)
...
3916 / 3915 = 1.0002554278416 (the remainder is 1, so 3915 is not a divisor of 3916)
3916 / 3916 = 1 (the remainder is 0, so 3916 is a divisor of 3916)

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 3916 (i.e. 62.577951388648). 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 $\frac{N}{d} = D$ )

3916 / 1 = 3916 (the remainder is 0, so 1 and 3916 are divisors of 3916)
3916 / 2 = 1958 (the remainder is 0, so 2 and 1958 are divisors of 3916)
3916 / 3 = 1305.3333333333 (the remainder is 1, so 3 is not a divisor of 3916)
...
3916 / 61 = 64.196721311475 (the remainder is 12, so 61 is not a divisor of 3916)
3916 / 62 = 63.161290322581 (the remainder is 10, so 62 is not a divisor of 3916)