What are the divisors of 2798?

1, 2, 1399, 2798

There is a total of 4 positive divisors.
The sum of these divisors is 4200.
The arithmetic mean is 1050.

2 even divisors

2, 2798

2 odd divisors

1, 1399

How to compute the divisors of 2798?

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 2798 by each of the numbers from 1 to 2798 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)

2798 / 1 = 2798 (the remainder is 0, so 1 is a divisor of 2798)
2798 / 2 = 1399 (the remainder is 0, so 2 is a divisor of 2798)
2798 / 3 = 932.66666666667 (the remainder is 2, so 3 is not a divisor of 2798)
...
2798 / 2797 = 1.0003575259206 (the remainder is 1, so 2797 is not a divisor of 2798)
2798 / 2798 = 1 (the remainder is 0, so 2798 is a divisor of 2798)

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 2798 (i.e. 52.896124621753). 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 $\frac{N}{d} = D$ )

2798 / 1 = 2798 (the remainder is 0, so 1 and 2798 are divisors of 2798)
2798 / 2 = 1399 (the remainder is 0, so 2 and 1399 are divisors of 2798)
2798 / 3 = 932.66666666667 (the remainder is 2, so 3 is not a divisor of 2798)
...
2798 / 51 = 54.862745098039 (the remainder is 44, so 51 is not a divisor of 2798)
2798 / 52 = 53.807692307692 (the remainder is 42, so 52 is not a divisor of 2798)