What are the divisors of 3566?

1, 2, 1783, 3566

There is a total of 4 positive divisors.
The sum of these divisors is 5352.
The arithmetic mean is 1338.

2 even divisors

2, 3566

2 odd divisors

1, 1783

How to compute the divisors of 3566?

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 3566 by each of the numbers from 1 to 3566 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)

3566 / 1 = 3566 (the remainder is 0, so 1 is a divisor of 3566)
3566 / 2 = 1783 (the remainder is 0, so 2 is a divisor of 3566)
3566 / 3 = 1188.6666666667 (the remainder is 2, so 3 is not a divisor of 3566)
...
3566 / 3565 = 1.0002805049088 (the remainder is 1, so 3565 is not a divisor of 3566)
3566 / 3566 = 1 (the remainder is 0, so 3566 is a divisor of 3566)

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 3566 (i.e. 59.715994507334). 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 $\frac{N}{d} = D$ )

3566 / 1 = 3566 (the remainder is 0, so 1 and 3566 are divisors of 3566)
3566 / 2 = 1783 (the remainder is 0, so 2 and 1783 are divisors of 3566)
3566 / 3 = 1188.6666666667 (the remainder is 2, so 3 is not a divisor of 3566)
...
3566 / 58 = 61.48275862069 (the remainder is 28, so 58 is not a divisor of 3566)
3566 / 59 = 60.440677966102 (the remainder is 26, so 59 is not a divisor of 3566)