What are the divisors of 499?

1, 499

There is a total of 2 positive divisors.
The sum of these divisors is 500.
The arithmetic mean is 250.

2 odd divisors

1, 499

How to compute the divisors of 499?

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 499 by each of the numbers from 1 to 499 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)

499 / 1 = 499 (the remainder is 0, so 1 is a divisor of 499)
499 / 2 = 249.5 (the remainder is 1, so 2 is not a divisor of 499)
499 / 3 = 166.33333333333 (the remainder is 1, so 3 is not a divisor of 499)
...
499 / 498 = 1.0020080321285 (the remainder is 1, so 498 is not a divisor of 499)
499 / 499 = 1 (the remainder is 0, so 499 is a divisor of 499)

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 499 (i.e. 22.338307903689). 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 $\frac{N}{d} = D$ )

499 / 1 = 499 (the remainder is 0, so 1 and 499 are divisors of 499)
499 / 2 = 249.5 (the remainder is 1, so 2 is not a divisor of 499)
499 / 3 = 166.33333333333 (the remainder is 1, so 3 is not a divisor of 499)
...
499 / 21 = 23.761904761905 (the remainder is 16, so 21 is not a divisor of 499)
499 / 22 = 22.681818181818 (the remainder is 15, so 22 is not a divisor of 499)