What are the divisors of 5521?

1, 5521

There is a total of 2 positive divisors.
The sum of these divisors is 5522.
The arithmetic mean is 2761.

2 odd divisors

1, 5521

How to compute the divisors of 5521?

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 5521 by each of the numbers from 1 to 5521 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)

5521 / 1 = 5521 (the remainder is 0, so 1 is a divisor of 5521)
5521 / 2 = 2760.5 (the remainder is 1, so 2 is not a divisor of 5521)
5521 / 3 = 1840.3333333333 (the remainder is 1, so 3 is not a divisor of 5521)
...
5521 / 5520 = 1.0001811594203 (the remainder is 1, so 5520 is not a divisor of 5521)
5521 / 5521 = 1 (the remainder is 0, so 5521 is a divisor of 5521)

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 5521 (i.e. 74.30343195304). 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 $\frac{N}{d} = D$ )

5521 / 1 = 5521 (the remainder is 0, so 1 and 5521 are divisors of 5521)
5521 / 2 = 2760.5 (the remainder is 1, so 2 is not a divisor of 5521)
5521 / 3 = 1840.3333333333 (the remainder is 1, so 3 is not a divisor of 5521)
...
5521 / 73 = 75.630136986301 (the remainder is 46, so 73 is not a divisor of 5521)
5521 / 74 = 74.608108108108 (the remainder is 45, so 74 is not a divisor of 5521)