What are the divisors of 5776?

1, 2, 4, 8, 16, 19, 38, 76, 152, 304, 361, 722, 1444, 2888, 5776

There is a total of 15 positive divisors.
The sum of these divisors is 11811.
The arithmetic mean is 787.4.

12 even divisors

2, 4, 8, 16, 38, 76, 152, 304, 722, 1444, 2888, 5776

3 odd divisors

1, 19, 361

How to compute the divisors of 5776?

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 5776 by each of the numbers from 1 to 5776 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)

5776 / 1 = 5776 (the remainder is 0, so 1 is a divisor of 5776)
5776 / 2 = 2888 (the remainder is 0, so 2 is a divisor of 5776)
5776 / 3 = 1925.3333333333 (the remainder is 1, so 3 is not a divisor of 5776)
...
5776 / 5775 = 1.0001731601732 (the remainder is 1, so 5775 is not a divisor of 5776)
5776 / 5776 = 1 (the remainder is 0, so 5776 is a divisor of 5776)

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 5776 (i.e. 76). 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 $\frac{N}{d} = D$ )

5776 / 1 = 5776 (the remainder is 0, so 1 and 5776 are divisors of 5776)
5776 / 2 = 2888 (the remainder is 0, so 2 and 2888 are divisors of 5776)
5776 / 3 = 1925.3333333333 (the remainder is 1, so 3 is not a divisor of 5776)
...
5776 / 75 = 77.013333333333 (the remainder is 1, so 75 is not a divisor of 5776)
5776 / 76 = 76 (the remainder is 0, so 76 and 76 are divisors of 5776)