What are the divisors of 3926?

1, 2, 13, 26, 151, 302, 1963, 3926

There is a total of 8 positive divisors.
The sum of these divisors is 6384.
The arithmetic mean is 798.

4 even divisors

2, 26, 302, 3926

4 odd divisors

1, 13, 151, 1963

How to compute the divisors of 3926?

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 3926 by each of the numbers from 1 to 3926 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)

3926 / 1 = 3926 (the remainder is 0, so 1 is a divisor of 3926)
3926 / 2 = 1963 (the remainder is 0, so 2 is a divisor of 3926)
3926 / 3 = 1308.6666666667 (the remainder is 2, so 3 is not a divisor of 3926)
...
3926 / 3925 = 1.0002547770701 (the remainder is 1, so 3925 is not a divisor of 3926)
3926 / 3926 = 1 (the remainder is 0, so 3926 is a divisor of 3926)

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 3926 (i.e. 62.657800791282). 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 $\frac{N}{d} = D$ )

3926 / 1 = 3926 (the remainder is 0, so 1 and 3926 are divisors of 3926)
3926 / 2 = 1963 (the remainder is 0, so 2 and 1963 are divisors of 3926)
3926 / 3 = 1308.6666666667 (the remainder is 2, so 3 is not a divisor of 3926)
...
3926 / 61 = 64.360655737705 (the remainder is 22, so 61 is not a divisor of 3926)
3926 / 62 = 63.322580645161 (the remainder is 20, so 62 is not a divisor of 3926)