What are the divisors of 1799?

1, 7, 257, 1799

There is a total of 4 positive divisors.
The sum of these divisors is 2064.
The arithmetic mean is 516.

4 odd divisors

1, 7, 257, 1799

How to compute the divisors of 1799?

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 1799 by each of the numbers from 1 to 1799 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)

1799 / 1 = 1799 (the remainder is 0, so 1 is a divisor of 1799)
1799 / 2 = 899.5 (the remainder is 1, so 2 is not a divisor of 1799)
1799 / 3 = 599.66666666667 (the remainder is 2, so 3 is not a divisor of 1799)
...
1799 / 1798 = 1.0005561735261 (the remainder is 1, so 1798 is not a divisor of 1799)
1799 / 1799 = 1 (the remainder is 0, so 1799 is a divisor of 1799)

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 1799 (i.e. 42.414620120897). 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 $\frac{N}{d} = D$ )

1799 / 1 = 1799 (the remainder is 0, so 1 and 1799 are divisors of 1799)
1799 / 2 = 899.5 (the remainder is 1, so 2 is not a divisor of 1799)
1799 / 3 = 599.66666666667 (the remainder is 2, so 3 is not a divisor of 1799)
...
1799 / 41 = 43.878048780488 (the remainder is 36, so 41 is not a divisor of 1799)
1799 / 42 = 42.833333333333 (the remainder is 35, so 42 is not a divisor of 1799)