What are the divisors of 5299?

1, 7, 757, 5299

There is a total of 4 positive divisors.
The sum of these divisors is 6064.
The arithmetic mean is 1516.

4 odd divisors

1, 7, 757, 5299

How to compute the divisors of 5299?

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 5299 by each of the numbers from 1 to 5299 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)

5299 / 1 = 5299 (the remainder is 0, so 1 is a divisor of 5299)
5299 / 2 = 2649.5 (the remainder is 1, so 2 is not a divisor of 5299)
5299 / 3 = 1766.3333333333 (the remainder is 1, so 3 is not a divisor of 5299)
...
5299 / 5298 = 1.0001887504719 (the remainder is 1, so 5298 is not a divisor of 5299)
5299 / 5299 = 1 (the remainder is 0, so 5299 is a divisor of 5299)

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 5299 (i.e. 72.794230540614). 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 $\frac{N}{d} = D$ )

5299 / 1 = 5299 (the remainder is 0, so 1 and 5299 are divisors of 5299)
5299 / 2 = 2649.5 (the remainder is 1, so 2 is not a divisor of 5299)
5299 / 3 = 1766.3333333333 (the remainder is 1, so 3 is not a divisor of 5299)
...
5299 / 71 = 74.633802816901 (the remainder is 45, so 71 is not a divisor of 5299)
5299 / 72 = 73.597222222222 (the remainder is 43, so 72 is not a divisor of 5299)