What are the divisors of 5522?

1, 2, 11, 22, 251, 502, 2761, 5522

There is a total of 8 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 1134.

4 even divisors

2, 22, 502, 5522

4 odd divisors

1, 11, 251, 2761

How to compute the divisors of 5522?

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 5522 by each of the numbers from 1 to 5522 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)

5522 / 1 = 5522 (the remainder is 0, so 1 is a divisor of 5522)
5522 / 2 = 2761 (the remainder is 0, so 2 is a divisor of 5522)
5522 / 3 = 1840.6666666667 (the remainder is 2, so 3 is not a divisor of 5522)
...
5522 / 5521 = 1.0001811266075 (the remainder is 1, so 5521 is not a divisor of 5522)
5522 / 5522 = 1 (the remainder is 0, so 5522 is a divisor of 5522)

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 5522 (i.e. 74.310160812637). 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 $\frac{N}{d} = D$ )

5522 / 1 = 5522 (the remainder is 0, so 1 and 5522 are divisors of 5522)
5522 / 2 = 2761 (the remainder is 0, so 2 and 2761 are divisors of 5522)
5522 / 3 = 1840.6666666667 (the remainder is 2, so 3 is not a divisor of 5522)
...
5522 / 73 = 75.643835616438 (the remainder is 47, so 73 is not a divisor of 5522)
5522 / 74 = 74.621621621622 (the remainder is 46, so 74 is not a divisor of 5522)