What are the divisors of 5549?

1, 31, 179, 5549

There is a total of 4 positive divisors.
The sum of these divisors is 5760.
The arithmetic mean is 1440.

4 odd divisors

1, 31, 179, 5549

How to compute the divisors of 5549?

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 5549 by each of the numbers from 1 to 5549 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)

5549 / 1 = 5549 (the remainder is 0, so 1 is a divisor of 5549)
5549 / 2 = 2774.5 (the remainder is 1, so 2 is not a divisor of 5549)
5549 / 3 = 1849.6666666667 (the remainder is 2, so 3 is not a divisor of 5549)
...
5549 / 5548 = 1.0001802451334 (the remainder is 1, so 5548 is not a divisor of 5549)
5549 / 5549 = 1 (the remainder is 0, so 5549 is a divisor of 5549)

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 5549 (i.e. 74.491610265855). 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 $\frac{N}{d} = D$ )

5549 / 1 = 5549 (the remainder is 0, so 1 and 5549 are divisors of 5549)
5549 / 2 = 2774.5 (the remainder is 1, so 2 is not a divisor of 5549)
5549 / 3 = 1849.6666666667 (the remainder is 2, so 3 is not a divisor of 5549)
...
5549 / 73 = 76.013698630137 (the remainder is 1, so 73 is not a divisor of 5549)
5549 / 74 = 74.986486486486 (the remainder is 73, so 74 is not a divisor of 5549)