What are the divisors of 3896?

1, 2, 4, 8, 487, 974, 1948, 3896

There is a total of 8 positive divisors.
The sum of these divisors is 7320.
The arithmetic mean is 915.

6 even divisors

2, 4, 8, 974, 1948, 3896

2 odd divisors

1, 487

How to compute the divisors of 3896?

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 3896 by each of the numbers from 1 to 3896 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)

3896 / 1 = 3896 (the remainder is 0, so 1 is a divisor of 3896)
3896 / 2 = 1948 (the remainder is 0, so 2 is a divisor of 3896)
3896 / 3 = 1298.6666666667 (the remainder is 2, so 3 is not a divisor of 3896)
...
3896 / 3895 = 1.0002567394095 (the remainder is 1, so 3895 is not a divisor of 3896)
3896 / 3896 = 1 (the remainder is 0, so 3896 is a divisor of 3896)

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 3896 (i.e. 62.417946137309). 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 $\frac{N}{d} = D$ )

3896 / 1 = 3896 (the remainder is 0, so 1 and 3896 are divisors of 3896)
3896 / 2 = 1948 (the remainder is 0, so 2 and 1948 are divisors of 3896)
3896 / 3 = 1298.6666666667 (the remainder is 2, so 3 is not a divisor of 3896)
...
3896 / 61 = 63.868852459016 (the remainder is 53, so 61 is not a divisor of 3896)
3896 / 62 = 62.838709677419 (the remainder is 52, so 62 is not a divisor of 3896)