What are the divisors of 3904?

1, 2, 4, 8, 16, 32, 61, 64, 122, 244, 488, 976, 1952, 3904

There is a total of 14 positive divisors.
The sum of these divisors is 7874.
The arithmetic mean is 562.42857142857.

12 even divisors

2, 4, 8, 16, 32, 64, 122, 244, 488, 976, 1952, 3904

2 odd divisors

1, 61

How to compute the divisors of 3904?

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 3904 by each of the numbers from 1 to 3904 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)

3904 / 1 = 3904 (the remainder is 0, so 1 is a divisor of 3904)
3904 / 2 = 1952 (the remainder is 0, so 2 is a divisor of 3904)
3904 / 3 = 1301.3333333333 (the remainder is 1, so 3 is not a divisor of 3904)
...
3904 / 3903 = 1.0002562131694 (the remainder is 1, so 3903 is not a divisor of 3904)
3904 / 3904 = 1 (the remainder is 0, so 3904 is a divisor of 3904)

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 3904 (i.e. 62.481997407253). 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 $\frac{N}{d} = D$ )

3904 / 1 = 3904 (the remainder is 0, so 1 and 3904 are divisors of 3904)
3904 / 2 = 1952 (the remainder is 0, so 2 and 1952 are divisors of 3904)
3904 / 3 = 1301.3333333333 (the remainder is 1, so 3 is not a divisor of 3904)
...
3904 / 61 = 64 (the remainder is 0, so 61 and 64 are divisors of 3904)
3904 / 62 = 62.967741935484 (the remainder is 60, so 62 is not a divisor of 3904)