What are the divisors of 1778?

1, 2, 7, 14, 127, 254, 889, 1778

There is a total of 8 positive divisors.
The sum of these divisors is 3072.
The arithmetic mean is 384.

4 even divisors

2, 14, 254, 1778

4 odd divisors

1, 7, 127, 889

How to compute the divisors of 1778?

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 1778 by each of the numbers from 1 to 1778 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)

1778 / 1 = 1778 (the remainder is 0, so 1 is a divisor of 1778)
1778 / 2 = 889 (the remainder is 0, so 2 is a divisor of 1778)
1778 / 3 = 592.66666666667 (the remainder is 2, so 3 is not a divisor of 1778)
...
1778 / 1777 = 1.0005627462015 (the remainder is 1, so 1777 is not a divisor of 1778)
1778 / 1778 = 1 (the remainder is 0, so 1778 is a divisor of 1778)

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 1778 (i.e. 42.166337284616). 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 $\frac{N}{d} = D$ )

1778 / 1 = 1778 (the remainder is 0, so 1 and 1778 are divisors of 1778)
1778 / 2 = 889 (the remainder is 0, so 2 and 889 are divisors of 1778)
1778 / 3 = 592.66666666667 (the remainder is 2, so 3 is not a divisor of 1778)
...
1778 / 41 = 43.365853658537 (the remainder is 15, so 41 is not a divisor of 1778)
1778 / 42 = 42.333333333333 (the remainder is 14, so 42 is not a divisor of 1778)