What are the divisors of 549?

1, 3, 9, 61, 183, 549

There is a total of 6 positive divisors.
The sum of these divisors is 806.
The arithmetic mean is 134.33333333333.

6 odd divisors

1, 3, 9, 61, 183, 549

How to compute the divisors of 549?

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 549 by each of the numbers from 1 to 549 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)

549 / 1 = 549 (the remainder is 0, so 1 is a divisor of 549)
549 / 2 = 274.5 (the remainder is 1, so 2 is not a divisor of 549)
549 / 3 = 183 (the remainder is 0, so 3 is a divisor of 549)
...
549 / 548 = 1.0018248175182 (the remainder is 1, so 548 is not a divisor of 549)
549 / 549 = 1 (the remainder is 0, so 549 is a divisor of 549)

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 549 (i.e. 23.43074902772). 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 $\frac{N}{d} = D$ )

549 / 1 = 549 (the remainder is 0, so 1 and 549 are divisors of 549)
549 / 2 = 274.5 (the remainder is 1, so 2 is not a divisor of 549)
549 / 3 = 183 (the remainder is 0, so 3 and 183 are divisors of 549)
...
549 / 22 = 24.954545454545 (the remainder is 21, so 22 is not a divisor of 549)
549 / 23 = 23.869565217391 (the remainder is 20, so 23 is not a divisor of 549)