What are the divisors of 3567?

1, 3, 29, 41, 87, 123, 1189, 3567

There is a total of 8 positive divisors.
The sum of these divisors is 5040.
The arithmetic mean is 630.

8 odd divisors

1, 3, 29, 41, 87, 123, 1189, 3567

How to compute the divisors of 3567?

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 3567 by each of the numbers from 1 to 3567 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)

3567 / 1 = 3567 (the remainder is 0, so 1 is a divisor of 3567)
3567 / 2 = 1783.5 (the remainder is 1, so 2 is not a divisor of 3567)
3567 / 3 = 1189 (the remainder is 0, so 3 is a divisor of 3567)
...
3567 / 3566 = 1.0002804262479 (the remainder is 1, so 3566 is not a divisor of 3567)
3567 / 3567 = 1 (the remainder is 0, so 3567 is a divisor of 3567)

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 3567 (i.e. 59.724366886556). 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 $\frac{N}{d} = D$ )

3567 / 1 = 3567 (the remainder is 0, so 1 and 3567 are divisors of 3567)
3567 / 2 = 1783.5 (the remainder is 1, so 2 is not a divisor of 3567)
3567 / 3 = 1189 (the remainder is 0, so 3 and 1189 are divisors of 3567)
...
3567 / 58 = 61.5 (the remainder is 29, so 58 is not a divisor of 3567)
3567 / 59 = 60.457627118644 (the remainder is 27, so 59 is not a divisor of 3567)