What are the divisors of 4549?

1, 4549

There is a total of 2 positive divisors.
The sum of these divisors is 4550.
The arithmetic mean is 2275.

2 odd divisors

1, 4549

How to compute the divisors of 4549?

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 4549 by each of the numbers from 1 to 4549 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)

4549 / 1 = 4549 (the remainder is 0, so 1 is a divisor of 4549)
4549 / 2 = 2274.5 (the remainder is 1, so 2 is not a divisor of 4549)
4549 / 3 = 1516.3333333333 (the remainder is 1, so 3 is not a divisor of 4549)
...
4549 / 4548 = 1.000219876869 (the remainder is 1, so 4548 is not a divisor of 4549)
4549 / 4549 = 1 (the remainder is 0, so 4549 is a divisor of 4549)

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 4549 (i.e. 67.446274915669). 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 $\frac{N}{d} = D$ )

4549 / 1 = 4549 (the remainder is 0, so 1 and 4549 are divisors of 4549)
4549 / 2 = 2274.5 (the remainder is 1, so 2 is not a divisor of 4549)
4549 / 3 = 1516.3333333333 (the remainder is 1, so 3 is not a divisor of 4549)
...
4549 / 66 = 68.924242424242 (the remainder is 61, so 66 is not a divisor of 4549)
4549 / 67 = 67.89552238806 (the remainder is 60, so 67 is not a divisor of 4549)