What are the divisors of 3956?

1, 2, 4, 23, 43, 46, 86, 92, 172, 989, 1978, 3956

There is a total of 12 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 616.

8 even divisors

2, 4, 46, 86, 92, 172, 1978, 3956

4 odd divisors

1, 23, 43, 989

How to compute the divisors of 3956?

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 3956 by each of the numbers from 1 to 3956 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)

3956 / 1 = 3956 (the remainder is 0, so 1 is a divisor of 3956)
3956 / 2 = 1978 (the remainder is 0, so 2 is a divisor of 3956)
3956 / 3 = 1318.6666666667 (the remainder is 2, so 3 is not a divisor of 3956)
...
3956 / 3955 = 1.0002528445006 (the remainder is 1, so 3955 is not a divisor of 3956)
3956 / 3956 = 1 (the remainder is 0, so 3956 is a divisor of 3956)

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 3956 (i.e. 62.896740774066). 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 $\frac{N}{d} = D$ )

3956 / 1 = 3956 (the remainder is 0, so 1 and 3956 are divisors of 3956)
3956 / 2 = 1978 (the remainder is 0, so 2 and 1978 are divisors of 3956)
3956 / 3 = 1318.6666666667 (the remainder is 2, so 3 is not a divisor of 3956)
...
3956 / 61 = 64.852459016393 (the remainder is 52, so 61 is not a divisor of 3956)
3956 / 62 = 63.806451612903 (the remainder is 50, so 62 is not a divisor of 3956)