What are the divisors of 3883?

1, 11, 353, 3883

There is a total of 4 positive divisors.
The sum of these divisors is 4248.
The arithmetic mean is 1062.

4 odd divisors

1, 11, 353, 3883

How to compute the divisors of 3883?

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 3883 by each of the numbers from 1 to 3883 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)

3883 / 1 = 3883 (the remainder is 0, so 1 is a divisor of 3883)
3883 / 2 = 1941.5 (the remainder is 1, so 2 is not a divisor of 3883)
3883 / 3 = 1294.3333333333 (the remainder is 1, so 3 is not a divisor of 3883)
...
3883 / 3882 = 1.0002575991757 (the remainder is 1, so 3882 is not a divisor of 3883)
3883 / 3883 = 1 (the remainder is 0, so 3883 is a divisor of 3883)

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 3883 (i.e. 62.313722405262). 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 $\frac{N}{d} = D$ )

3883 / 1 = 3883 (the remainder is 0, so 1 and 3883 are divisors of 3883)
3883 / 2 = 1941.5 (the remainder is 1, so 2 is not a divisor of 3883)
3883 / 3 = 1294.3333333333 (the remainder is 1, so 3 is not a divisor of 3883)
...
3883 / 61 = 63.655737704918 (the remainder is 40, so 61 is not a divisor of 3883)
3883 / 62 = 62.629032258065 (the remainder is 39, so 62 is not a divisor of 3883)