What are the divisors of 2887?

1, 2887

There is a total of 2 positive divisors.
The sum of these divisors is 2888.
The arithmetic mean is 1444.

2 odd divisors

1, 2887

How to compute the divisors of 2887?

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 2887 by each of the numbers from 1 to 2887 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)

2887 / 1 = 2887 (the remainder is 0, so 1 is a divisor of 2887)
2887 / 2 = 1443.5 (the remainder is 1, so 2 is not a divisor of 2887)
2887 / 3 = 962.33333333333 (the remainder is 1, so 3 is not a divisor of 2887)
...
2887 / 2886 = 1.0003465003465 (the remainder is 1, so 2886 is not a divisor of 2887)
2887 / 2887 = 1 (the remainder is 0, so 2887 is a divisor of 2887)

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 2887 (i.e. 53.730810528039). 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 $\frac{N}{d} = D$ )

2887 / 1 = 2887 (the remainder is 0, so 1 and 2887 are divisors of 2887)
2887 / 2 = 1443.5 (the remainder is 1, so 2 is not a divisor of 2887)
2887 / 3 = 962.33333333333 (the remainder is 1, so 3 is not a divisor of 2887)
...
2887 / 52 = 55.519230769231 (the remainder is 27, so 52 is not a divisor of 2887)
2887 / 53 = 54.471698113208 (the remainder is 25, so 53 is not a divisor of 2887)