What are the divisors of 5563?

1, 5563

There is a total of 2 positive divisors.
The sum of these divisors is 5564.
The arithmetic mean is 2782.

2 odd divisors

1, 5563

How to compute the divisors of 5563?

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 5563 by each of the numbers from 1 to 5563 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)

5563 / 1 = 5563 (the remainder is 0, so 1 is a divisor of 5563)
5563 / 2 = 2781.5 (the remainder is 1, so 2 is not a divisor of 5563)
5563 / 3 = 1854.3333333333 (the remainder is 1, so 3 is not a divisor of 5563)
...
5563 / 5562 = 1.0001797914419 (the remainder is 1, so 5562 is not a divisor of 5563)
5563 / 5563 = 1 (the remainder is 0, so 5563 is a divisor of 5563)

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 5563 (i.e. 74.585521383175). 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 $\frac{N}{d} = D$ )

5563 / 1 = 5563 (the remainder is 0, so 1 and 5563 are divisors of 5563)
5563 / 2 = 2781.5 (the remainder is 1, so 2 is not a divisor of 5563)
5563 / 3 = 1854.3333333333 (the remainder is 1, so 3 is not a divisor of 5563)
...
5563 / 73 = 76.205479452055 (the remainder is 15, so 73 is not a divisor of 5563)
5563 / 74 = 75.175675675676 (the remainder is 13, so 74 is not a divisor of 5563)