What are the divisors of 1787?

1, 1787

There is a total of 2 positive divisors.
The sum of these divisors is 1788.
The arithmetic mean is 894.

2 odd divisors

1, 1787

How to compute the divisors of 1787?

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 1787 by each of the numbers from 1 to 1787 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)

1787 / 1 = 1787 (the remainder is 0, so 1 is a divisor of 1787)
1787 / 2 = 893.5 (the remainder is 1, so 2 is not a divisor of 1787)
1787 / 3 = 595.66666666667 (the remainder is 2, so 3 is not a divisor of 1787)
...
1787 / 1786 = 1.0005599104143 (the remainder is 1, so 1786 is not a divisor of 1787)
1787 / 1787 = 1 (the remainder is 0, so 1787 is a divisor of 1787)

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 1787 (i.e. 42.272922775697). 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 $\frac{N}{d} = D$ )

1787 / 1 = 1787 (the remainder is 0, so 1 and 1787 are divisors of 1787)
1787 / 2 = 893.5 (the remainder is 1, so 2 is not a divisor of 1787)
1787 / 3 = 595.66666666667 (the remainder is 2, so 3 is not a divisor of 1787)
...
1787 / 41 = 43.585365853659 (the remainder is 24, so 41 is not a divisor of 1787)
1787 / 42 = 42.547619047619 (the remainder is 23, so 42 is not a divisor of 1787)