What are the divisors of 5285?

1, 5, 7, 35, 151, 755, 1057, 5285

There is a total of 8 positive divisors.
The sum of these divisors is 7296.
The arithmetic mean is 912.

8 odd divisors

1, 5, 7, 35, 151, 755, 1057, 5285

How to compute the divisors of 5285?

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 5285 by each of the numbers from 1 to 5285 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)

5285 / 1 = 5285 (the remainder is 0, so 1 is a divisor of 5285)
5285 / 2 = 2642.5 (the remainder is 1, so 2 is not a divisor of 5285)
5285 / 3 = 1761.6666666667 (the remainder is 2, so 3 is not a divisor of 5285)
...
5285 / 5284 = 1.0001892505678 (the remainder is 1, so 5284 is not a divisor of 5285)
5285 / 5285 = 1 (the remainder is 0, so 5285 is a divisor of 5285)

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 5285 (i.e. 72.698005474703). 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 $\frac{N}{d} = D$ )

5285 / 1 = 5285 (the remainder is 0, so 1 and 5285 are divisors of 5285)
5285 / 2 = 2642.5 (the remainder is 1, so 2 is not a divisor of 5285)
5285 / 3 = 1761.6666666667 (the remainder is 2, so 3 is not a divisor of 5285)
...
5285 / 71 = 74.43661971831 (the remainder is 31, so 71 is not a divisor of 5285)
5285 / 72 = 73.402777777778 (the remainder is 29, so 72 is not a divisor of 5285)