What are the divisors of 5297?

1, 5297

There is a total of 2 positive divisors.
The sum of these divisors is 5298.
The arithmetic mean is 2649.

2 odd divisors

1, 5297

How to compute the divisors of 5297?

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 5297 by each of the numbers from 1 to 5297 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)

5297 / 1 = 5297 (the remainder is 0, so 1 is a divisor of 5297)
5297 / 2 = 2648.5 (the remainder is 1, so 2 is not a divisor of 5297)
5297 / 3 = 1765.6666666667 (the remainder is 2, so 3 is not a divisor of 5297)
...
5297 / 5296 = 1.0001888217523 (the remainder is 1, so 5296 is not a divisor of 5297)
5297 / 5297 = 1 (the remainder is 0, so 5297 is a divisor of 5297)

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 5297 (i.e. 72.780491891715). 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 $\frac{N}{d} = D$ )

5297 / 1 = 5297 (the remainder is 0, so 1 and 5297 are divisors of 5297)
5297 / 2 = 2648.5 (the remainder is 1, so 2 is not a divisor of 5297)
5297 / 3 = 1765.6666666667 (the remainder is 2, so 3 is not a divisor of 5297)
...
5297 / 71 = 74.605633802817 (the remainder is 43, so 71 is not a divisor of 5297)
5297 / 72 = 73.569444444444 (the remainder is 41, so 72 is not a divisor of 5297)