What are the divisors of 1720?

1, 2, 4, 5, 8, 10, 20, 40, 43, 86, 172, 215, 344, 430, 860, 1720

There is a total of 16 positive divisors.
The sum of these divisors is 3960.
The arithmetic mean is 247.5.

12 even divisors

2, 4, 8, 10, 20, 40, 86, 172, 344, 430, 860, 1720

4 odd divisors

1, 5, 43, 215

How to compute the divisors of 1720?

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 1720 by each of the numbers from 1 to 1720 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)

1720 / 1 = 1720 (the remainder is 0, so 1 is a divisor of 1720)
1720 / 2 = 860 (the remainder is 0, so 2 is a divisor of 1720)
1720 / 3 = 573.33333333333 (the remainder is 1, so 3 is not a divisor of 1720)
...
1720 / 1719 = 1.000581733566 (the remainder is 1, so 1719 is not a divisor of 1720)
1720 / 1720 = 1 (the remainder is 0, so 1720 is a divisor of 1720)

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 1720 (i.e. 41.472882706655). 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 $\frac{N}{d} = D$ )

1720 / 1 = 1720 (the remainder is 0, so 1 and 1720 are divisors of 1720)
1720 / 2 = 860 (the remainder is 0, so 2 and 860 are divisors of 1720)
1720 / 3 = 573.33333333333 (the remainder is 1, so 3 is not a divisor of 1720)
...
1720 / 40 = 43 (the remainder is 0, so 40 and 43 are divisors of 1720)
1720 / 41 = 41.951219512195 (the remainder is 39, so 41 is not a divisor of 1720)