What are the divisors of 5133?

1, 3, 29, 59, 87, 177, 1711, 5133

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

8 odd divisors

1, 3, 29, 59, 87, 177, 1711, 5133

How to compute the divisors of 5133?

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 5133 by each of the numbers from 1 to 5133 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)

5133 / 1 = 5133 (the remainder is 0, so 1 is a divisor of 5133)
5133 / 2 = 2566.5 (the remainder is 1, so 2 is not a divisor of 5133)
5133 / 3 = 1711 (the remainder is 0, so 3 is a divisor of 5133)
...
5133 / 5132 = 1.0001948558067 (the remainder is 1, so 5132 is not a divisor of 5133)
5133 / 5133 = 1 (the remainder is 0, so 5133 is a divisor of 5133)

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 5133 (i.e. 71.644957952392). 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 $\frac{N}{d} = D$ )

5133 / 1 = 5133 (the remainder is 0, so 1 and 5133 are divisors of 5133)
5133 / 2 = 2566.5 (the remainder is 1, so 2 is not a divisor of 5133)
5133 / 3 = 1711 (the remainder is 0, so 3 and 1711 are divisors of 5133)
...
5133 / 70 = 73.328571428571 (the remainder is 23, so 70 is not a divisor of 5133)
5133 / 71 = 72.295774647887 (the remainder is 21, so 71 is not a divisor of 5133)