What are the divisors of 3560?

1, 2, 4, 5, 8, 10, 20, 40, 89, 178, 356, 445, 712, 890, 1780, 3560

There is a total of 16 positive divisors.
The sum of these divisors is 8100.
The arithmetic mean is 506.25.

12 even divisors

2, 4, 8, 10, 20, 40, 178, 356, 712, 890, 1780, 3560

4 odd divisors

1, 5, 89, 445

How to compute the divisors of 3560?

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 3560 by each of the numbers from 1 to 3560 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)

3560 / 1 = 3560 (the remainder is 0, so 1 is a divisor of 3560)
3560 / 2 = 1780 (the remainder is 0, so 2 is a divisor of 3560)
3560 / 3 = 1186.6666666667 (the remainder is 2, so 3 is not a divisor of 3560)
...
3560 / 3559 = 1.0002809778028 (the remainder is 1, so 3559 is not a divisor of 3560)
3560 / 3560 = 1 (the remainder is 0, so 3560 is a divisor of 3560)

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 3560 (i.e. 59.665735560705). 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 $\frac{N}{d} = D$ )

3560 / 1 = 3560 (the remainder is 0, so 1 and 3560 are divisors of 3560)
3560 / 2 = 1780 (the remainder is 0, so 2 and 1780 are divisors of 3560)
3560 / 3 = 1186.6666666667 (the remainder is 2, so 3 is not a divisor of 3560)
...
3560 / 58 = 61.379310344828 (the remainder is 22, so 58 is not a divisor of 3560)
3560 / 59 = 60.338983050847 (the remainder is 20, so 59 is not a divisor of 3560)