What are the divisors of 3884?

1, 2, 4, 971, 1942, 3884

There is a total of 6 positive divisors.
The sum of these divisors is 6804.
The arithmetic mean is 1134.

4 even divisors

2, 4, 1942, 3884

2 odd divisors

1, 971

How to compute the divisors of 3884?

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 3884 by each of the numbers from 1 to 3884 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)

3884 / 1 = 3884 (the remainder is 0, so 1 is a divisor of 3884)
3884 / 2 = 1942 (the remainder is 0, so 2 is a divisor of 3884)
3884 / 3 = 1294.6666666667 (the remainder is 2, so 3 is not a divisor of 3884)
...
3884 / 3883 = 1.0002575328354 (the remainder is 1, so 3883 is not a divisor of 3884)
3884 / 3884 = 1 (the remainder is 0, so 3884 is a divisor of 3884)

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 3884 (i.e. 62.321745803532). 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 $\frac{N}{d} = D$ )

3884 / 1 = 3884 (the remainder is 0, so 1 and 3884 are divisors of 3884)
3884 / 2 = 1942 (the remainder is 0, so 2 and 1942 are divisors of 3884)
3884 / 3 = 1294.6666666667 (the remainder is 2, so 3 is not a divisor of 3884)
...
3884 / 61 = 63.672131147541 (the remainder is 41, so 61 is not a divisor of 3884)
3884 / 62 = 62.645161290323 (the remainder is 40, so 62 is not a divisor of 3884)