What are the divisors of 1641?

1, 3, 547, 1641

There is a total of 4 positive divisors.
The sum of these divisors is 2192.
The arithmetic mean is 548.

4 odd divisors

1, 3, 547, 1641

How to compute the divisors of 1641?

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 1641 by each of the numbers from 1 to 1641 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)

1641 / 1 = 1641 (the remainder is 0, so 1 is a divisor of 1641)
1641 / 2 = 820.5 (the remainder is 1, so 2 is not a divisor of 1641)
1641 / 3 = 547 (the remainder is 0, so 3 is a divisor of 1641)
...
1641 / 1640 = 1.0006097560976 (the remainder is 1, so 1640 is not a divisor of 1641)
1641 / 1641 = 1 (the remainder is 0, so 1641 is a divisor of 1641)

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 1641 (i.e. 40.509258201058). 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 $\frac{N}{d} = D$ )

1641 / 1 = 1641 (the remainder is 0, so 1 and 1641 are divisors of 1641)
1641 / 2 = 820.5 (the remainder is 1, so 2 is not a divisor of 1641)
1641 / 3 = 547 (the remainder is 0, so 3 and 547 are divisors of 1641)
...
1641 / 39 = 42.076923076923 (the remainder is 3, so 39 is not a divisor of 1641)
1641 / 40 = 41.025 (the remainder is 1, so 40 is not a divisor of 1641)