What are the divisors of 5553?

1, 3, 9, 617, 1851, 5553

There is a total of 6 positive divisors.
The sum of these divisors is 8034.
The arithmetic mean is 1339.

6 odd divisors

1, 3, 9, 617, 1851, 5553

How to compute the divisors of 5553?

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 5553 by each of the numbers from 1 to 5553 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)

5553 / 1 = 5553 (the remainder is 0, so 1 is a divisor of 5553)
5553 / 2 = 2776.5 (the remainder is 1, so 2 is not a divisor of 5553)
5553 / 3 = 1851 (the remainder is 0, so 3 is a divisor of 5553)
...
5553 / 5552 = 1.0001801152738 (the remainder is 1, so 5552 is not a divisor of 5553)
5553 / 5553 = 1 (the remainder is 0, so 5553 is a divisor of 5553)

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 5553 (i.e. 74.518454090245). 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 $\frac{N}{d} = D$ )

5553 / 1 = 5553 (the remainder is 0, so 1 and 5553 are divisors of 5553)
5553 / 2 = 2776.5 (the remainder is 1, so 2 is not a divisor of 5553)
5553 / 3 = 1851 (the remainder is 0, so 3 and 1851 are divisors of 5553)
...
5553 / 73 = 76.068493150685 (the remainder is 5, so 73 is not a divisor of 5553)
5553 / 74 = 75.040540540541 (the remainder is 3, so 74 is not a divisor of 5553)