What are the divisors of 5680?

1, 2, 4, 5, 8, 10, 16, 20, 40, 71, 80, 142, 284, 355, 568, 710, 1136, 1420, 2840, 5680

There is a total of 20 positive divisors.
The sum of these divisors is 13392.
The arithmetic mean is 669.6.

16 even divisors

2, 4, 8, 10, 16, 20, 40, 80, 142, 284, 568, 710, 1136, 1420, 2840, 5680

4 odd divisors

1, 5, 71, 355

How to compute the divisors of 5680?

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 5680 by each of the numbers from 1 to 5680 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)

5680 / 1 = 5680 (the remainder is 0, so 1 is a divisor of 5680)
5680 / 2 = 2840 (the remainder is 0, so 2 is a divisor of 5680)
5680 / 3 = 1893.3333333333 (the remainder is 1, so 3 is not a divisor of 5680)
...
5680 / 5679 = 1.0001760873393 (the remainder is 1, so 5679 is not a divisor of 5680)
5680 / 5680 = 1 (the remainder is 0, so 5680 is a divisor of 5680)

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 5680 (i.e. 75.365774725667). 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 $\frac{N}{d} = D$ )

5680 / 1 = 5680 (the remainder is 0, so 1 and 5680 are divisors of 5680)
5680 / 2 = 2840 (the remainder is 0, so 2 and 2840 are divisors of 5680)
5680 / 3 = 1893.3333333333 (the remainder is 1, so 3 is not a divisor of 5680)
...
5680 / 74 = 76.756756756757 (the remainder is 56, so 74 is not a divisor of 5680)
5680 / 75 = 75.733333333333 (the remainder is 55, so 75 is not a divisor of 5680)