What are the divisors of 3568?

1, 2, 4, 8, 16, 223, 446, 892, 1784, 3568

There is a total of 10 positive divisors.
The sum of these divisors is 6944.
The arithmetic mean is 694.4.

8 even divisors

2, 4, 8, 16, 446, 892, 1784, 3568

2 odd divisors

1, 223

How to compute the divisors of 3568?

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 3568 by each of the numbers from 1 to 3568 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)

3568 / 1 = 3568 (the remainder is 0, so 1 is a divisor of 3568)
3568 / 2 = 1784 (the remainder is 0, so 2 is a divisor of 3568)
3568 / 3 = 1189.3333333333 (the remainder is 1, so 3 is not a divisor of 3568)
...
3568 / 3567 = 1.0002803476311 (the remainder is 1, so 3567 is not a divisor of 3568)
3568 / 3568 = 1 (the remainder is 0, so 3568 is a divisor of 3568)

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 3568 (i.e. 59.732738092272). 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 $\frac{N}{d} = D$ )

3568 / 1 = 3568 (the remainder is 0, so 1 and 3568 are divisors of 3568)
3568 / 2 = 1784 (the remainder is 0, so 2 and 1784 are divisors of 3568)
3568 / 3 = 1189.3333333333 (the remainder is 1, so 3 is not a divisor of 3568)
...
3568 / 58 = 61.51724137931 (the remainder is 30, so 58 is not a divisor of 3568)
3568 / 59 = 60.474576271186 (the remainder is 28, so 59 is not a divisor of 3568)