What are the divisors of 5546?

1, 2, 47, 59, 94, 118, 2773, 5546

There is a total of 8 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 1080.

4 even divisors

2, 94, 118, 5546

4 odd divisors

1, 47, 59, 2773

How to compute the divisors of 5546?

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 5546 by each of the numbers from 1 to 5546 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)

5546 / 1 = 5546 (the remainder is 0, so 1 is a divisor of 5546)
5546 / 2 = 2773 (the remainder is 0, so 2 is a divisor of 5546)
5546 / 3 = 1848.6666666667 (the remainder is 2, so 3 is not a divisor of 5546)
...
5546 / 5545 = 1.000180342651 (the remainder is 1, so 5545 is not a divisor of 5546)
5546 / 5546 = 1 (the remainder is 0, so 5546 is a divisor of 5546)

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 5546 (i.e. 74.471471047643). 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 $\frac{N}{d} = D$ )

5546 / 1 = 5546 (the remainder is 0, so 1 and 5546 are divisors of 5546)
5546 / 2 = 2773 (the remainder is 0, so 2 and 2773 are divisors of 5546)
5546 / 3 = 1848.6666666667 (the remainder is 2, so 3 is not a divisor of 5546)
...
5546 / 73 = 75.972602739726 (the remainder is 71, so 73 is not a divisor of 5546)
5546 / 74 = 74.945945945946 (the remainder is 70, so 74 is not a divisor of 5546)