What are the divisors of 1771?

1, 7, 11, 23, 77, 161, 253, 1771

There is a total of 8 positive divisors.
The sum of these divisors is 2304.
The arithmetic mean is 288.

8 odd divisors

1, 7, 11, 23, 77, 161, 253, 1771

How to compute the divisors of 1771?

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 1771 by each of the numbers from 1 to 1771 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)

1771 / 1 = 1771 (the remainder is 0, so 1 is a divisor of 1771)
1771 / 2 = 885.5 (the remainder is 1, so 2 is not a divisor of 1771)
1771 / 3 = 590.33333333333 (the remainder is 1, so 3 is not a divisor of 1771)
...
1771 / 1770 = 1.0005649717514 (the remainder is 1, so 1770 is not a divisor of 1771)
1771 / 1771 = 1 (the remainder is 0, so 1771 is a divisor of 1771)

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 1771 (i.e. 42.083250825002). 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 $\frac{N}{d} = D$ )

1771 / 1 = 1771 (the remainder is 0, so 1 and 1771 are divisors of 1771)
1771 / 2 = 885.5 (the remainder is 1, so 2 is not a divisor of 1771)
1771 / 3 = 590.33333333333 (the remainder is 1, so 3 is not a divisor of 1771)
...
1771 / 41 = 43.19512195122 (the remainder is 8, so 41 is not a divisor of 1771)
1771 / 42 = 42.166666666667 (the remainder is 7, so 42 is not a divisor of 1771)