What are the divisors of 1774?

1, 2, 887, 1774

There is a total of 4 positive divisors.
The sum of these divisors is 2664.
The arithmetic mean is 666.

2 even divisors

2, 1774

2 odd divisors

1, 887

How to compute the divisors of 1774?

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 1774 by each of the numbers from 1 to 1774 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)

1774 / 1 = 1774 (the remainder is 0, so 1 is a divisor of 1774)
1774 / 2 = 887 (the remainder is 0, so 2 is a divisor of 1774)
1774 / 3 = 591.33333333333 (the remainder is 1, so 3 is not a divisor of 1774)
...
1774 / 1773 = 1.0005640157924 (the remainder is 1, so 1773 is not a divisor of 1774)
1774 / 1774 = 1 (the remainder is 0, so 1774 is a divisor of 1774)

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 1774 (i.e. 42.118879377305). 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 $\frac{N}{d} = D$ )

1774 / 1 = 1774 (the remainder is 0, so 1 and 1774 are divisors of 1774)
1774 / 2 = 887 (the remainder is 0, so 2 and 887 are divisors of 1774)
1774 / 3 = 591.33333333333 (the remainder is 1, so 3 is not a divisor of 1774)
...
1774 / 41 = 43.268292682927 (the remainder is 11, so 41 is not a divisor of 1774)
1774 / 42 = 42.238095238095 (the remainder is 10, so 42 is not a divisor of 1774)