What are the divisors of 5132?

1, 2, 4, 1283, 2566, 5132

There is a total of 6 positive divisors.
The sum of these divisors is 8988.
The arithmetic mean is 1498.

4 even divisors

2, 4, 2566, 5132

2 odd divisors

1, 1283

How to compute the divisors of 5132?

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 5132 by each of the numbers from 1 to 5132 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)

5132 / 1 = 5132 (the remainder is 0, so 1 is a divisor of 5132)
5132 / 2 = 2566 (the remainder is 0, so 2 is a divisor of 5132)
5132 / 3 = 1710.6666666667 (the remainder is 2, so 3 is not a divisor of 5132)
...
5132 / 5131 = 1.0001948937829 (the remainder is 1, so 5131 is not a divisor of 5132)
5132 / 5132 = 1 (the remainder is 0, so 5132 is a divisor of 5132)

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 5132 (i.e. 71.637978754289). 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 $\frac{N}{d} = D$ )

5132 / 1 = 5132 (the remainder is 0, so 1 and 5132 are divisors of 5132)
5132 / 2 = 2566 (the remainder is 0, so 2 and 2566 are divisors of 5132)
5132 / 3 = 1710.6666666667 (the remainder is 2, so 3 is not a divisor of 5132)
...
5132 / 70 = 73.314285714286 (the remainder is 22, so 70 is not a divisor of 5132)
5132 / 71 = 72.281690140845 (the remainder is 20, so 71 is not a divisor of 5132)