What are the divisors of 5322?

1, 2, 3, 6, 887, 1774, 2661, 5322

There is a total of 8 positive divisors.
The sum of these divisors is 10656.
The arithmetic mean is 1332.

4 even divisors

2, 6, 1774, 5322

4 odd divisors

1, 3, 887, 2661

How to compute the divisors of 5322?

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 5322 by each of the numbers from 1 to 5322 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)

5322 / 1 = 5322 (the remainder is 0, so 1 is a divisor of 5322)
5322 / 2 = 2661 (the remainder is 0, so 2 is a divisor of 5322)
5322 / 3 = 1774 (the remainder is 0, so 3 is a divisor of 5322)
...
5322 / 5321 = 1.0001879345988 (the remainder is 1, so 5321 is not a divisor of 5322)
5322 / 5322 = 1 (the remainder is 0, so 5322 is a divisor of 5322)

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 5322 (i.e. 72.952039039358). 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 $\frac{N}{d} = D$ )

5322 / 1 = 5322 (the remainder is 0, so 1 and 5322 are divisors of 5322)
5322 / 2 = 2661 (the remainder is 0, so 2 and 2661 are divisors of 5322)
5322 / 3 = 1774 (the remainder is 0, so 3 and 1774 are divisors of 5322)
...
5322 / 71 = 74.957746478873 (the remainder is 68, so 71 is not a divisor of 5322)
5322 / 72 = 73.916666666667 (the remainder is 66, so 72 is not a divisor of 5322)