What are the divisors of 5097?

1, 3, 1699, 5097

There is a total of 4 positive divisors.
The sum of these divisors is 6800.
The arithmetic mean is 1700.

4 odd divisors

1, 3, 1699, 5097

How to compute the divisors of 5097?

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 5097 by each of the numbers from 1 to 5097 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)

5097 / 1 = 5097 (the remainder is 0, so 1 is a divisor of 5097)
5097 / 2 = 2548.5 (the remainder is 1, so 2 is not a divisor of 5097)
5097 / 3 = 1699 (the remainder is 0, so 3 is a divisor of 5097)
...
5097 / 5096 = 1.0001962323391 (the remainder is 1, so 5096 is not a divisor of 5097)
5097 / 5097 = 1 (the remainder is 0, so 5097 is a divisor of 5097)

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 5097 (i.e. 71.393276994406). 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 $\frac{N}{d} = D$ )

5097 / 1 = 5097 (the remainder is 0, so 1 and 5097 are divisors of 5097)
5097 / 2 = 2548.5 (the remainder is 1, so 2 is not a divisor of 5097)
5097 / 3 = 1699 (the remainder is 0, so 3 and 1699 are divisors of 5097)
...
5097 / 70 = 72.814285714286 (the remainder is 57, so 70 is not a divisor of 5097)
5097 / 71 = 71.788732394366 (the remainder is 56, so 71 is not a divisor of 5097)