What are the divisors of 5330?

1, 2, 5, 10, 13, 26, 41, 65, 82, 130, 205, 410, 533, 1066, 2665, 5330

There is a total of 16 positive divisors.
The sum of these divisors is 10584.
The arithmetic mean is 661.5.

8 even divisors

2, 10, 26, 82, 130, 410, 1066, 5330

8 odd divisors

1, 5, 13, 41, 65, 205, 533, 2665

How to compute the divisors of 5330?

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 5330 by each of the numbers from 1 to 5330 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)

5330 / 1 = 5330 (the remainder is 0, so 1 is a divisor of 5330)
5330 / 2 = 2665 (the remainder is 0, so 2 is a divisor of 5330)
5330 / 3 = 1776.6666666667 (the remainder is 2, so 3 is not a divisor of 5330)
...
5330 / 5329 = 1.0001876524676 (the remainder is 1, so 5329 is not a divisor of 5330)
5330 / 5330 = 1 (the remainder is 0, so 5330 is a divisor of 5330)

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 5330 (i.e. 73.006848993776). 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 $\frac{N}{d} = D$ )

5330 / 1 = 5330 (the remainder is 0, so 1 and 5330 are divisors of 5330)
5330 / 2 = 2665 (the remainder is 0, so 2 and 2665 are divisors of 5330)
5330 / 3 = 1776.6666666667 (the remainder is 2, so 3 is not a divisor of 5330)
...
5330 / 72 = 74.027777777778 (the remainder is 2, so 72 is not a divisor of 5330)
5330 / 73 = 73.013698630137 (the remainder is 1, so 73 is not a divisor of 5330)