What are the divisors of 5557?

1, 5557

There is a total of 2 positive divisors.
The sum of these divisors is 5558.
The arithmetic mean is 2779.

2 odd divisors

1, 5557

How to compute the divisors of 5557?

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 5557 by each of the numbers from 1 to 5557 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)

5557 / 1 = 5557 (the remainder is 0, so 1 is a divisor of 5557)
5557 / 2 = 2778.5 (the remainder is 1, so 2 is not a divisor of 5557)
5557 / 3 = 1852.3333333333 (the remainder is 1, so 3 is not a divisor of 5557)
...
5557 / 5556 = 1.0001799856012 (the remainder is 1, so 5556 is not a divisor of 5557)
5557 / 5557 = 1 (the remainder is 0, so 5557 is a divisor of 5557)

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 5557 (i.e. 74.545288248152). 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 $\frac{N}{d} = D$ )

5557 / 1 = 5557 (the remainder is 0, so 1 and 5557 are divisors of 5557)
5557 / 2 = 2778.5 (the remainder is 1, so 2 is not a divisor of 5557)
5557 / 3 = 1852.3333333333 (the remainder is 1, so 3 is not a divisor of 5557)
...
5557 / 73 = 76.123287671233 (the remainder is 9, so 73 is not a divisor of 5557)
5557 / 74 = 75.094594594595 (the remainder is 7, so 74 is not a divisor of 5557)