What are the divisors of 5578?

1, 2, 2789, 5578

There is a total of 4 positive divisors.
The sum of these divisors is 8370.
The arithmetic mean is 2092.5.

2 even divisors

2, 5578

2 odd divisors

1, 2789

How to compute the divisors of 5578?

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 5578 by each of the numbers from 1 to 5578 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)

5578 / 1 = 5578 (the remainder is 0, so 1 is a divisor of 5578)
5578 / 2 = 2789 (the remainder is 0, so 2 is a divisor of 5578)
5578 / 3 = 1859.3333333333 (the remainder is 1, so 3 is not a divisor of 5578)
...
5578 / 5577 = 1.0001793078716 (the remainder is 1, so 5577 is not a divisor of 5578)
5578 / 5578 = 1 (the remainder is 0, so 5578 is a divisor of 5578)

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 5578 (i.e. 74.686009399351). 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 $\frac{N}{d} = D$ )

5578 / 1 = 5578 (the remainder is 0, so 1 and 5578 are divisors of 5578)
5578 / 2 = 2789 (the remainder is 0, so 2 and 2789 are divisors of 5578)
5578 / 3 = 1859.3333333333 (the remainder is 1, so 3 is not a divisor of 5578)
...
5578 / 73 = 76.41095890411 (the remainder is 30, so 73 is not a divisor of 5578)
5578 / 74 = 75.378378378378 (the remainder is 28, so 74 is not a divisor of 5578)