What are the divisors of 3920?

1, 2, 4, 5, 7, 8, 10, 14, 16, 20, 28, 35, 40, 49, 56, 70, 80, 98, 112, 140, 196, 245, 280, 392, 490, 560, 784, 980, 1960, 3920

There is a total of 30 positive divisors.
The sum of these divisors is 10602.
The arithmetic mean is 353.4.

24 even divisors

2, 4, 8, 10, 14, 16, 20, 28, 40, 56, 70, 80, 98, 112, 140, 196, 280, 392, 490, 560, 784, 980, 1960, 3920

6 odd divisors

1, 5, 7, 35, 49, 245

How to compute the divisors of 3920?

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 3920 by each of the numbers from 1 to 3920 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)

3920 / 1 = 3920 (the remainder is 0, so 1 is a divisor of 3920)
3920 / 2 = 1960 (the remainder is 0, so 2 is a divisor of 3920)
3920 / 3 = 1306.6666666667 (the remainder is 2, so 3 is not a divisor of 3920)
...
3920 / 3919 = 1.0002551671345 (the remainder is 1, so 3919 is not a divisor of 3920)
3920 / 3920 = 1 (the remainder is 0, so 3920 is a divisor of 3920)

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 3920 (i.e. 62.609903369994). 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 $\frac{N}{d} = D$ )

3920 / 1 = 3920 (the remainder is 0, so 1 and 3920 are divisors of 3920)
3920 / 2 = 1960 (the remainder is 0, so 2 and 1960 are divisors of 3920)
3920 / 3 = 1306.6666666667 (the remainder is 2, so 3 is not a divisor of 3920)
...
3920 / 61 = 64.262295081967 (the remainder is 16, so 61 is not a divisor of 3920)
3920 / 62 = 63.225806451613 (the remainder is 14, so 62 is not a divisor of 3920)