What are the divisors of 1880?

1, 2, 4, 5, 8, 10, 20, 40, 47, 94, 188, 235, 376, 470, 940, 1880

There is a total of 16 positive divisors.
The sum of these divisors is 4320.
The arithmetic mean is 270.

12 even divisors

2, 4, 8, 10, 20, 40, 94, 188, 376, 470, 940, 1880

4 odd divisors

1, 5, 47, 235

How to compute the divisors of 1880?

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 1880 by each of the numbers from 1 to 1880 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)

1880 / 1 = 1880 (the remainder is 0, so 1 is a divisor of 1880)
1880 / 2 = 940 (the remainder is 0, so 2 is a divisor of 1880)
1880 / 3 = 626.66666666667 (the remainder is 2, so 3 is not a divisor of 1880)
...
1880 / 1879 = 1.0005321979776 (the remainder is 1, so 1879 is not a divisor of 1880)
1880 / 1880 = 1 (the remainder is 0, so 1880 is a divisor of 1880)

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 1880 (i.e. 43.358966777358). 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 $\frac{N}{d} = D$ )

1880 / 1 = 1880 (the remainder is 0, so 1 and 1880 are divisors of 1880)
1880 / 2 = 940 (the remainder is 0, so 2 and 940 are divisors of 1880)
1880 / 3 = 626.66666666667 (the remainder is 2, so 3 is not a divisor of 1880)
...
1880 / 42 = 44.761904761905 (the remainder is 32, so 42 is not a divisor of 1880)
1880 / 43 = 43.720930232558 (the remainder is 31, so 43 is not a divisor of 1880)