What are the divisors of 3889?

1, 3889

There is a total of 2 positive divisors.
The sum of these divisors is 3890.
The arithmetic mean is 1945.

2 odd divisors

1, 3889

How to compute the divisors of 3889?

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 3889 by each of the numbers from 1 to 3889 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)

3889 / 1 = 3889 (the remainder is 0, so 1 is a divisor of 3889)
3889 / 2 = 1944.5 (the remainder is 1, so 2 is not a divisor of 3889)
3889 / 3 = 1296.3333333333 (the remainder is 1, so 3 is not a divisor of 3889)
...
3889 / 3888 = 1.0002572016461 (the remainder is 1, so 3888 is not a divisor of 3889)
3889 / 3889 = 1 (the remainder is 0, so 3889 is a divisor of 3889)

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 3889 (i.e. 62.361847310675). 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 $\frac{N}{d} = D$ )

3889 / 1 = 3889 (the remainder is 0, so 1 and 3889 are divisors of 3889)
3889 / 2 = 1944.5 (the remainder is 1, so 2 is not a divisor of 3889)
3889 / 3 = 1296.3333333333 (the remainder is 1, so 3 is not a divisor of 3889)
...
3889 / 61 = 63.754098360656 (the remainder is 46, so 61 is not a divisor of 3889)
3889 / 62 = 62.725806451613 (the remainder is 45, so 62 is not a divisor of 3889)