What are the divisors of 5215?

1, 5, 7, 35, 149, 745, 1043, 5215

There is a total of 8 positive divisors.
The sum of these divisors is 7200.
The arithmetic mean is 900.

8 odd divisors

1, 5, 7, 35, 149, 745, 1043, 5215

How to compute the divisors of 5215?

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 5215 by each of the numbers from 1 to 5215 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)

5215 / 1 = 5215 (the remainder is 0, so 1 is a divisor of 5215)
5215 / 2 = 2607.5 (the remainder is 1, so 2 is not a divisor of 5215)
5215 / 3 = 1738.3333333333 (the remainder is 1, so 3 is not a divisor of 5215)
...
5215 / 5214 = 1.000191791331 (the remainder is 1, so 5214 is not a divisor of 5215)
5215 / 5215 = 1 (the remainder is 0, so 5215 is a divisor of 5215)

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 5215 (i.e. 72.214956899523). 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 $\frac{N}{d} = D$ )

5215 / 1 = 5215 (the remainder is 0, so 1 and 5215 are divisors of 5215)
5215 / 2 = 2607.5 (the remainder is 1, so 2 is not a divisor of 5215)
5215 / 3 = 1738.3333333333 (the remainder is 1, so 3 is not a divisor of 5215)
...
5215 / 71 = 73.450704225352 (the remainder is 32, so 71 is not a divisor of 5215)
5215 / 72 = 72.430555555556 (the remainder is 31, so 72 is not a divisor of 5215)