What are the divisors of 1659?

1, 3, 7, 21, 79, 237, 553, 1659

There is a total of 8 positive divisors.
The sum of these divisors is 2560.
The arithmetic mean is 320.

8 odd divisors

1, 3, 7, 21, 79, 237, 553, 1659

How to compute the divisors of 1659?

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 1659 by each of the numbers from 1 to 1659 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)

1659 / 1 = 1659 (the remainder is 0, so 1 is a divisor of 1659)
1659 / 2 = 829.5 (the remainder is 1, so 2 is not a divisor of 1659)
1659 / 3 = 553 (the remainder is 0, so 3 is a divisor of 1659)
...
1659 / 1658 = 1.0006031363088 (the remainder is 1, so 1658 is not a divisor of 1659)
1659 / 1659 = 1 (the remainder is 0, so 1659 is a divisor of 1659)

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 1659 (i.e. 40.730823708833). 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 $\frac{N}{d} = D$ )

1659 / 1 = 1659 (the remainder is 0, so 1 and 1659 are divisors of 1659)
1659 / 2 = 829.5 (the remainder is 1, so 2 is not a divisor of 1659)
1659 / 3 = 553 (the remainder is 0, so 3 and 553 are divisors of 1659)
...
1659 / 39 = 42.538461538462 (the remainder is 21, so 39 is not a divisor of 1659)
1659 / 40 = 41.475 (the remainder is 19, so 40 is not a divisor of 1659)