What are the divisors of 1776?

1, 2, 3, 4, 6, 8, 12, 16, 24, 37, 48, 74, 111, 148, 222, 296, 444, 592, 888, 1776

There is a total of 20 positive divisors.
The sum of these divisors is 4712.
The arithmetic mean is 235.6.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 74, 148, 222, 296, 444, 592, 888, 1776

4 odd divisors

1, 3, 37, 111

How to compute the divisors of 1776?

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 1776 by each of the numbers from 1 to 1776 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)

1776 / 1 = 1776 (the remainder is 0, so 1 is a divisor of 1776)
1776 / 2 = 888 (the remainder is 0, so 2 is a divisor of 1776)
1776 / 3 = 592 (the remainder is 0, so 3 is a divisor of 1776)
...
1776 / 1775 = 1.0005633802817 (the remainder is 1, so 1775 is not a divisor of 1776)
1776 / 1776 = 1 (the remainder is 0, so 1776 is a divisor of 1776)

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 1776 (i.e. 42.142615011411). 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 $\frac{N}{d} = D$ )

1776 / 1 = 1776 (the remainder is 0, so 1 and 1776 are divisors of 1776)
1776 / 2 = 888 (the remainder is 0, so 2 and 888 are divisors of 1776)
1776 / 3 = 592 (the remainder is 0, so 3 and 592 are divisors of 1776)
...
1776 / 41 = 43.317073170732 (the remainder is 13, so 41 is not a divisor of 1776)
1776 / 42 = 42.285714285714 (the remainder is 12, so 42 is not a divisor of 1776)