What are the divisors of 5527?

1, 5527

There is a total of 2 positive divisors.
The sum of these divisors is 5528.
The arithmetic mean is 2764.

2 odd divisors

1, 5527

How to compute the divisors of 5527?

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 5527 by each of the numbers from 1 to 5527 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)

5527 / 1 = 5527 (the remainder is 0, so 1 is a divisor of 5527)
5527 / 2 = 2763.5 (the remainder is 1, so 2 is not a divisor of 5527)
5527 / 3 = 1842.3333333333 (the remainder is 1, so 3 is not a divisor of 5527)
...
5527 / 5526 = 1.0001809627217 (the remainder is 1, so 5526 is not a divisor of 5527)
5527 / 5527 = 1 (the remainder is 0, so 5527 is a divisor of 5527)

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 5527 (i.e. 74.343795975185). 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 $\frac{N}{d} = D$ )

5527 / 1 = 5527 (the remainder is 0, so 1 and 5527 are divisors of 5527)
5527 / 2 = 2763.5 (the remainder is 1, so 2 is not a divisor of 5527)
5527 / 3 = 1842.3333333333 (the remainder is 1, so 3 is not a divisor of 5527)
...
5527 / 73 = 75.712328767123 (the remainder is 52, so 73 is not a divisor of 5527)
5527 / 74 = 74.689189189189 (the remainder is 51, so 74 is not a divisor of 5527)