What are the divisors of 1520?

1, 2, 4, 5, 8, 10, 16, 19, 20, 38, 40, 76, 80, 95, 152, 190, 304, 380, 760, 1520

There is a total of 20 positive divisors.
The sum of these divisors is 3720.
The arithmetic mean is 186.

16 even divisors

2, 4, 8, 10, 16, 20, 38, 40, 76, 80, 152, 190, 304, 380, 760, 1520

4 odd divisors

1, 5, 19, 95

How to compute the divisors of 1520?

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 1520 by each of the numbers from 1 to 1520 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)

1520 / 1 = 1520 (the remainder is 0, so 1 is a divisor of 1520)
1520 / 2 = 760 (the remainder is 0, so 2 is a divisor of 1520)
1520 / 3 = 506.66666666667 (the remainder is 2, so 3 is not a divisor of 1520)
...
1520 / 1519 = 1.0006583278473 (the remainder is 1, so 1519 is not a divisor of 1520)
1520 / 1520 = 1 (the remainder is 0, so 1520 is a divisor of 1520)

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 1520 (i.e. 38.987177379236). 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 $\frac{N}{d} = D$ )

1520 / 1 = 1520 (the remainder is 0, so 1 and 1520 are divisors of 1520)
1520 / 2 = 760 (the remainder is 0, so 2 and 760 are divisors of 1520)
1520 / 3 = 506.66666666667 (the remainder is 2, so 3 is not a divisor of 1520)
...
1520 / 37 = 41.081081081081 (the remainder is 3, so 37 is not a divisor of 1520)
1520 / 38 = 40 (the remainder is 0, so 38 and 40 are divisors of 1520)