What are the divisors of 3581?

1, 3581

There is a total of 2 positive divisors.
The sum of these divisors is 3582.
The arithmetic mean is 1791.

2 odd divisors

1, 3581

How to compute the divisors of 3581?

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 3581 by each of the numbers from 1 to 3581 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)

3581 / 1 = 3581 (the remainder is 0, so 1 is a divisor of 3581)
3581 / 2 = 1790.5 (the remainder is 1, so 2 is not a divisor of 3581)
3581 / 3 = 1193.6666666667 (the remainder is 2, so 3 is not a divisor of 3581)
...
3581 / 3580 = 1.0002793296089 (the remainder is 1, so 3580 is not a divisor of 3581)
3581 / 3581 = 1 (the remainder is 0, so 3581 is a divisor of 3581)

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 3581 (i.e. 59.841457201509). 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 $\frac{N}{d} = D$ )

3581 / 1 = 3581 (the remainder is 0, so 1 and 3581 are divisors of 3581)
3581 / 2 = 1790.5 (the remainder is 1, so 2 is not a divisor of 3581)
3581 / 3 = 1193.6666666667 (the remainder is 2, so 3 is not a divisor of 3581)
...
3581 / 58 = 61.741379310345 (the remainder is 43, so 58 is not a divisor of 3581)
3581 / 59 = 60.694915254237 (the remainder is 41, so 59 is not a divisor of 3581)