What are the divisors of 3591?

1, 3, 7, 9, 19, 21, 27, 57, 63, 133, 171, 189, 399, 513, 1197, 3591

There is a total of 16 positive divisors.
The sum of these divisors is 6400.
The arithmetic mean is 400.

16 odd divisors

1, 3, 7, 9, 19, 21, 27, 57, 63, 133, 171, 189, 399, 513, 1197, 3591

How to compute the divisors of 3591?

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 3591 by each of the numbers from 1 to 3591 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)

3591 / 1 = 3591 (the remainder is 0, so 1 is a divisor of 3591)
3591 / 2 = 1795.5 (the remainder is 1, so 2 is not a divisor of 3591)
3591 / 3 = 1197 (the remainder is 0, so 3 is a divisor of 3591)
...
3591 / 3590 = 1.000278551532 (the remainder is 1, so 3590 is not a divisor of 3591)
3591 / 3591 = 1 (the remainder is 0, so 3591 is a divisor of 3591)

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 3591 (i.e. 59.924953066315). 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 $\frac{N}{d} = D$ )

3591 / 1 = 3591 (the remainder is 0, so 1 and 3591 are divisors of 3591)
3591 / 2 = 1795.5 (the remainder is 1, so 2 is not a divisor of 3591)
3591 / 3 = 1197 (the remainder is 0, so 3 and 1197 are divisors of 3591)
...
3591 / 58 = 61.913793103448 (the remainder is 53, so 58 is not a divisor of 3591)
3591 / 59 = 60.864406779661 (the remainder is 51, so 59 is not a divisor of 3591)