What are the divisors of 1860?

1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 31, 60, 62, 93, 124, 155, 186, 310, 372, 465, 620, 930, 1860

There is a total of 24 positive divisors.
The sum of these divisors is 5376.
The arithmetic mean is 224.

16 even divisors

2, 4, 6, 10, 12, 20, 30, 60, 62, 124, 186, 310, 372, 620, 930, 1860

8 odd divisors

1, 3, 5, 15, 31, 93, 155, 465

How to compute the divisors of 1860?

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 1860 by each of the numbers from 1 to 1860 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)

1860 / 1 = 1860 (the remainder is 0, so 1 is a divisor of 1860)
1860 / 2 = 930 (the remainder is 0, so 2 is a divisor of 1860)
1860 / 3 = 620 (the remainder is 0, so 3 is a divisor of 1860)
...
1860 / 1859 = 1.0005379236148 (the remainder is 1, so 1859 is not a divisor of 1860)
1860 / 1860 = 1 (the remainder is 0, so 1860 is a divisor of 1860)

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 1860 (i.e. 43.127717305696). 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 $\frac{N}{d} = D$ )

1860 / 1 = 1860 (the remainder is 0, so 1 and 1860 are divisors of 1860)
1860 / 2 = 930 (the remainder is 0, so 2 and 930 are divisors of 1860)
1860 / 3 = 620 (the remainder is 0, so 3 and 620 are divisors of 1860)
...
1860 / 42 = 44.285714285714 (the remainder is 12, so 42 is not a divisor of 1860)
1860 / 43 = 43.255813953488 (the remainder is 11, so 43 is not a divisor of 1860)