What are the divisors of 2837?

1, 2837

There is a total of 2 positive divisors.
The sum of these divisors is 2838.
The arithmetic mean is 1419.

2 odd divisors

1, 2837

How to compute the divisors of 2837?

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 2837 by each of the numbers from 1 to 2837 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)

2837 / 1 = 2837 (the remainder is 0, so 1 is a divisor of 2837)
2837 / 2 = 1418.5 (the remainder is 1, so 2 is not a divisor of 2837)
2837 / 3 = 945.66666666667 (the remainder is 2, so 3 is not a divisor of 2837)
...
2837 / 2836 = 1.0003526093089 (the remainder is 1, so 2836 is not a divisor of 2837)
2837 / 2837 = 1 (the remainder is 0, so 2837 is a divisor of 2837)

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 2837 (i.e. 53.263495942343). 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 $\frac{N}{d} = D$ )

2837 / 1 = 2837 (the remainder is 0, so 1 and 2837 are divisors of 2837)
2837 / 2 = 1418.5 (the remainder is 1, so 2 is not a divisor of 2837)
2837 / 3 = 945.66666666667 (the remainder is 2, so 3 is not a divisor of 2837)
...
2837 / 52 = 54.557692307692 (the remainder is 29, so 52 is not a divisor of 2837)
2837 / 53 = 53.528301886792 (the remainder is 28, so 53 is not a divisor of 2837)