What are the divisors of 5562?

1, 2, 3, 6, 9, 18, 27, 54, 103, 206, 309, 618, 927, 1854, 2781, 5562

There is a total of 16 positive divisors.
The sum of these divisors is 12480.
The arithmetic mean is 780.

8 even divisors

2, 6, 18, 54, 206, 618, 1854, 5562

8 odd divisors

1, 3, 9, 27, 103, 309, 927, 2781

How to compute the divisors of 5562?

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 5562 by each of the numbers from 1 to 5562 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)

5562 / 1 = 5562 (the remainder is 0, so 1 is a divisor of 5562)
5562 / 2 = 2781 (the remainder is 0, so 2 is a divisor of 5562)
5562 / 3 = 1854 (the remainder is 0, so 3 is a divisor of 5562)
...
5562 / 5561 = 1.0001798237727 (the remainder is 1, so 5561 is not a divisor of 5562)
5562 / 5562 = 1 (the remainder is 0, so 5562 is a divisor of 5562)

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 5562 (i.e. 74.578817367936). 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 $\frac{N}{d} = D$ )

5562 / 1 = 5562 (the remainder is 0, so 1 and 5562 are divisors of 5562)
5562 / 2 = 2781 (the remainder is 0, so 2 and 2781 are divisors of 5562)
5562 / 3 = 1854 (the remainder is 0, so 3 and 1854 are divisors of 5562)
...
5562 / 73 = 76.191780821918 (the remainder is 14, so 73 is not a divisor of 5562)
5562 / 74 = 75.162162162162 (the remainder is 12, so 74 is not a divisor of 5562)