What are the divisors of 5577?

1, 3, 11, 13, 33, 39, 143, 169, 429, 507, 1859, 5577

There is a total of 12 positive divisors.
The sum of these divisors is 8784.
The arithmetic mean is 732.

12 odd divisors

1, 3, 11, 13, 33, 39, 143, 169, 429, 507, 1859, 5577

How to compute the divisors of 5577?

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 5577 by each of the numbers from 1 to 5577 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)

5577 / 1 = 5577 (the remainder is 0, so 1 is a divisor of 5577)
5577 / 2 = 2788.5 (the remainder is 1, so 2 is not a divisor of 5577)
5577 / 3 = 1859 (the remainder is 0, so 3 is a divisor of 5577)
...
5577 / 5576 = 1.0001793400287 (the remainder is 1, so 5576 is not a divisor of 5577)
5577 / 5577 = 1 (the remainder is 0, so 5577 is a divisor of 5577)

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 5577 (i.e. 74.679314404994). 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 $\frac{N}{d} = D$ )

5577 / 1 = 5577 (the remainder is 0, so 1 and 5577 are divisors of 5577)
5577 / 2 = 2788.5 (the remainder is 1, so 2 is not a divisor of 5577)
5577 / 3 = 1859 (the remainder is 0, so 3 and 1859 are divisors of 5577)
...
5577 / 73 = 76.397260273973 (the remainder is 29, so 73 is not a divisor of 5577)
5577 / 74 = 75.364864864865 (the remainder is 27, so 74 is not a divisor of 5577)