What are the divisors of 5574?

1, 2, 3, 6, 929, 1858, 2787, 5574

There is a total of 8 positive divisors.
The sum of these divisors is 11160.
The arithmetic mean is 1395.

4 even divisors

2, 6, 1858, 5574

4 odd divisors

1, 3, 929, 2787

How to compute the divisors of 5574?

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 5574 by each of the numbers from 1 to 5574 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)

5574 / 1 = 5574 (the remainder is 0, so 1 is a divisor of 5574)
5574 / 2 = 2787 (the remainder is 0, so 2 is a divisor of 5574)
5574 / 3 = 1858 (the remainder is 0, so 3 is a divisor of 5574)
...
5574 / 5573 = 1.0001794365692 (the remainder is 1, so 5573 is not a divisor of 5574)
5574 / 5574 = 1 (the remainder is 0, so 5574 is a divisor of 5574)

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 5574 (i.e. 74.65922581972). 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 $\frac{N}{d} = D$ )

5574 / 1 = 5574 (the remainder is 0, so 1 and 5574 are divisors of 5574)
5574 / 2 = 2787 (the remainder is 0, so 2 and 2787 are divisors of 5574)
5574 / 3 = 1858 (the remainder is 0, so 3 and 1858 are divisors of 5574)
...
5574 / 73 = 76.356164383562 (the remainder is 26, so 73 is not a divisor of 5574)
5574 / 74 = 75.324324324324 (the remainder is 24, so 74 is not a divisor of 5574)