What are the divisors of 2839?

1, 17, 167, 2839

There is a total of 4 positive divisors.
The sum of these divisors is 3024.
The arithmetic mean is 756.

4 odd divisors

1, 17, 167, 2839

How to compute the divisors of 2839?

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 2839 by each of the numbers from 1 to 2839 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)

2839 / 1 = 2839 (the remainder is 0, so 1 is a divisor of 2839)
2839 / 2 = 1419.5 (the remainder is 1, so 2 is not a divisor of 2839)
2839 / 3 = 946.33333333333 (the remainder is 1, so 3 is not a divisor of 2839)
...
2839 / 2838 = 1.0003523608175 (the remainder is 1, so 2838 is not a divisor of 2839)
2839 / 2839 = 1 (the remainder is 0, so 2839 is a divisor of 2839)

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 2839 (i.e. 53.282267219029). 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 $\frac{N}{d} = D$ )

2839 / 1 = 2839 (the remainder is 0, so 1 and 2839 are divisors of 2839)
2839 / 2 = 1419.5 (the remainder is 1, so 2 is not a divisor of 2839)
2839 / 3 = 946.33333333333 (the remainder is 1, so 3 is not a divisor of 2839)
...
2839 / 52 = 54.596153846154 (the remainder is 31, so 52 is not a divisor of 2839)
2839 / 53 = 53.566037735849 (the remainder is 30, so 53 is not a divisor of 2839)