What are the divisors of 1798?

1, 2, 29, 31, 58, 62, 899, 1798

There is a total of 8 positive divisors.
The sum of these divisors is 2880.
The arithmetic mean is 360.

4 even divisors

2, 58, 62, 1798

4 odd divisors

1, 29, 31, 899

How to compute the divisors of 1798?

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 1798 by each of the numbers from 1 to 1798 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)

1798 / 1 = 1798 (the remainder is 0, so 1 is a divisor of 1798)
1798 / 2 = 899 (the remainder is 0, so 2 is a divisor of 1798)
1798 / 3 = 599.33333333333 (the remainder is 1, so 3 is not a divisor of 1798)
...
1798 / 1797 = 1.0005564830273 (the remainder is 1, so 1797 is not a divisor of 1798)
1798 / 1798 = 1 (the remainder is 0, so 1798 is a divisor of 1798)

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 1798 (i.e. 42.402830094228). 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 $\frac{N}{d} = D$ )

1798 / 1 = 1798 (the remainder is 0, so 1 and 1798 are divisors of 1798)
1798 / 2 = 899 (the remainder is 0, so 2 and 899 are divisors of 1798)
1798 / 3 = 599.33333333333 (the remainder is 1, so 3 is not a divisor of 1798)
...
1798 / 41 = 43.853658536585 (the remainder is 35, so 41 is not a divisor of 1798)
1798 / 42 = 42.809523809524 (the remainder is 34, so 42 is not a divisor of 1798)