What are the divisors of 3583?

1, 3583

There is a total of 2 positive divisors.
The sum of these divisors is 3584.
The arithmetic mean is 1792.

2 odd divisors

1, 3583

How to compute the divisors of 3583?

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 3583 by each of the numbers from 1 to 3583 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)

3583 / 1 = 3583 (the remainder is 0, so 1 is a divisor of 3583)
3583 / 2 = 1791.5 (the remainder is 1, so 2 is not a divisor of 3583)
3583 / 3 = 1194.3333333333 (the remainder is 1, so 3 is not a divisor of 3583)
...
3583 / 3582 = 1.000279173646 (the remainder is 1, so 3582 is not a divisor of 3583)
3583 / 3583 = 1 (the remainder is 0, so 3583 is a divisor of 3583)

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 3583 (i.e. 59.858165691909). 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 $\frac{N}{d} = D$ )

3583 / 1 = 3583 (the remainder is 0, so 1 and 3583 are divisors of 3583)
3583 / 2 = 1791.5 (the remainder is 1, so 2 is not a divisor of 3583)
3583 / 3 = 1194.3333333333 (the remainder is 1, so 3 is not a divisor of 3583)
...
3583 / 58 = 61.775862068966 (the remainder is 45, so 58 is not a divisor of 3583)
3583 / 59 = 60.728813559322 (the remainder is 43, so 59 is not a divisor of 3583)