What are the divisors of 1568?

1, 2, 4, 7, 8, 14, 16, 28, 32, 49, 56, 98, 112, 196, 224, 392, 784, 1568

There is a total of 18 positive divisors.
The sum of these divisors is 3591.
The arithmetic mean is 199.5.

15 even divisors

2, 4, 8, 14, 16, 28, 32, 56, 98, 112, 196, 224, 392, 784, 1568

3 odd divisors

1, 7, 49

How to compute the divisors of 1568?

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 1568 by each of the numbers from 1 to 1568 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)

1568 / 1 = 1568 (the remainder is 0, so 1 is a divisor of 1568)
1568 / 2 = 784 (the remainder is 0, so 2 is a divisor of 1568)
1568 / 3 = 522.66666666667 (the remainder is 2, so 3 is not a divisor of 1568)
...
1568 / 1567 = 1.0006381620932 (the remainder is 1, so 1567 is not a divisor of 1568)
1568 / 1568 = 1 (the remainder is 0, so 1568 is a divisor of 1568)

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 1568 (i.e. 39.597979746447). 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 $\frac{N}{d} = D$ )

1568 / 1 = 1568 (the remainder is 0, so 1 and 1568 are divisors of 1568)
1568 / 2 = 784 (the remainder is 0, so 2 and 784 are divisors of 1568)
1568 / 3 = 522.66666666667 (the remainder is 2, so 3 is not a divisor of 1568)
...
1568 / 38 = 41.263157894737 (the remainder is 10, so 38 is not a divisor of 1568)
1568 / 39 = 40.205128205128 (the remainder is 8, so 39 is not a divisor of 1568)