What are the divisors of 1655?

1, 5, 331, 1655

There is a total of 4 positive divisors.
The sum of these divisors is 1992.
The arithmetic mean is 498.

4 odd divisors

1, 5, 331, 1655

How to compute the divisors of 1655?

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 1655 by each of the numbers from 1 to 1655 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)

1655 / 1 = 1655 (the remainder is 0, so 1 is a divisor of 1655)
1655 / 2 = 827.5 (the remainder is 1, so 2 is not a divisor of 1655)
1655 / 3 = 551.66666666667 (the remainder is 2, so 3 is not a divisor of 1655)
...
1655 / 1654 = 1.0006045949214 (the remainder is 1, so 1654 is not a divisor of 1655)
1655 / 1655 = 1 (the remainder is 0, so 1655 is a divisor of 1655)

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 1655 (i.e. 40.681691213616). 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 $\frac{N}{d} = D$ )

1655 / 1 = 1655 (the remainder is 0, so 1 and 1655 are divisors of 1655)
1655 / 2 = 827.5 (the remainder is 1, so 2 is not a divisor of 1655)
1655 / 3 = 551.66666666667 (the remainder is 2, so 3 is not a divisor of 1655)
...
1655 / 39 = 42.435897435897 (the remainder is 17, so 39 is not a divisor of 1655)
1655 / 40 = 41.375 (the remainder is 15, so 40 is not a divisor of 1655)