What are the divisors of 3928?

1, 2, 4, 8, 491, 982, 1964, 3928

There is a total of 8 positive divisors.
The sum of these divisors is 7380.
The arithmetic mean is 922.5.

6 even divisors

2, 4, 8, 982, 1964, 3928

2 odd divisors

1, 491

How to compute the divisors of 3928?

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 3928 by each of the numbers from 1 to 3928 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)

3928 / 1 = 3928 (the remainder is 0, so 1 is a divisor of 3928)
3928 / 2 = 1964 (the remainder is 0, so 2 is a divisor of 3928)
3928 / 3 = 1309.3333333333 (the remainder is 1, so 3 is not a divisor of 3928)
...
3928 / 3927 = 1.0002546473135 (the remainder is 1, so 3927 is not a divisor of 3928)
3928 / 3928 = 1 (the remainder is 0, so 3928 is a divisor of 3928)

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 3928 (i.e. 62.67375846397). 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 $\frac{N}{d} = D$ )

3928 / 1 = 3928 (the remainder is 0, so 1 and 3928 are divisors of 3928)
3928 / 2 = 1964 (the remainder is 0, so 2 and 1964 are divisors of 3928)
3928 / 3 = 1309.3333333333 (the remainder is 1, so 3 is not a divisor of 3928)
...
3928 / 61 = 64.393442622951 (the remainder is 24, so 61 is not a divisor of 3928)
3928 / 62 = 63.354838709677 (the remainder is 22, so 62 is not a divisor of 3928)