What are the divisors of 799?

1, 17, 47, 799

There is a total of 4 positive divisors.
The sum of these divisors is 864.
The arithmetic mean is 216.

4 odd divisors

1, 17, 47, 799

How to compute the divisors of 799?

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 799 by each of the numbers from 1 to 799 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)

799 / 1 = 799 (the remainder is 0, so 1 is a divisor of 799)
799 / 2 = 399.5 (the remainder is 1, so 2 is not a divisor of 799)
799 / 3 = 266.33333333333 (the remainder is 1, so 3 is not a divisor of 799)
...
799 / 798 = 1.0012531328321 (the remainder is 1, so 798 is not a divisor of 799)
799 / 799 = 1 (the remainder is 0, so 799 is a divisor of 799)

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 799 (i.e. 28.266588050205). 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 $\frac{N}{d} = D$ )

799 / 1 = 799 (the remainder is 0, so 1 and 799 are divisors of 799)
799 / 2 = 399.5 (the remainder is 1, so 2 is not a divisor of 799)
799 / 3 = 266.33333333333 (the remainder is 1, so 3 is not a divisor of 799)
...
799 / 27 = 29.592592592593 (the remainder is 16, so 27 is not a divisor of 799)
799 / 28 = 28.535714285714 (the remainder is 15, so 28 is not a divisor of 799)