What are the divisors of 5331?

1, 3, 1777, 5331

There is a total of 4 positive divisors.
The sum of these divisors is 7112.
The arithmetic mean is 1778.

4 odd divisors

1, 3, 1777, 5331

How to compute the divisors of 5331?

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 5331 by each of the numbers from 1 to 5331 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)

5331 / 1 = 5331 (the remainder is 0, so 1 is a divisor of 5331)
5331 / 2 = 2665.5 (the remainder is 1, so 2 is not a divisor of 5331)
5331 / 3 = 1777 (the remainder is 0, so 3 is a divisor of 5331)
...
5331 / 5330 = 1.0001876172608 (the remainder is 1, so 5330 is not a divisor of 5331)
5331 / 5331 = 1 (the remainder is 0, so 5331 is a divisor of 5331)

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 5331 (i.e. 73.013697345087). 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 $\frac{N}{d} = D$ )

5331 / 1 = 5331 (the remainder is 0, so 1 and 5331 are divisors of 5331)
5331 / 2 = 2665.5 (the remainder is 1, so 2 is not a divisor of 5331)
5331 / 3 = 1777 (the remainder is 0, so 3 and 1777 are divisors of 5331)
...
5331 / 72 = 74.041666666667 (the remainder is 3, so 72 is not a divisor of 5331)
5331 / 73 = 73.027397260274 (the remainder is 2, so 73 is not a divisor of 5331)