What are the divisors of 5099?

1, 5099

There is a total of 2 positive divisors.
The sum of these divisors is 5100.
The arithmetic mean is 2550.

2 odd divisors

1, 5099

How to compute the divisors of 5099?

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 5099 by each of the numbers from 1 to 5099 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)

5099 / 1 = 5099 (the remainder is 0, so 1 is a divisor of 5099)
5099 / 2 = 2549.5 (the remainder is 1, so 2 is not a divisor of 5099)
5099 / 3 = 1699.6666666667 (the remainder is 2, so 3 is not a divisor of 5099)
...
5099 / 5098 = 1.000196155355 (the remainder is 1, so 5098 is not a divisor of 5099)
5099 / 5099 = 1 (the remainder is 0, so 5099 is a divisor of 5099)

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 5099 (i.e. 71.407282541769). 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 $\frac{N}{d} = D$ )

5099 / 1 = 5099 (the remainder is 0, so 1 and 5099 are divisors of 5099)
5099 / 2 = 2549.5 (the remainder is 1, so 2 is not a divisor of 5099)
5099 / 3 = 1699.6666666667 (the remainder is 2, so 3 is not a divisor of 5099)
...
5099 / 70 = 72.842857142857 (the remainder is 59, so 70 is not a divisor of 5099)
5099 / 71 = 71.816901408451 (the remainder is 58, so 71 is not a divisor of 5099)