What are the divisors of 2030?

1, 2, 5, 7, 10, 14, 29, 35, 58, 70, 145, 203, 290, 406, 1015, 2030

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

8 even divisors

2, 10, 14, 58, 70, 290, 406, 2030

8 odd divisors

1, 5, 7, 29, 35, 145, 203, 1015

How to compute the divisors of 2030?

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 2030 by each of the numbers from 1 to 2030 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)

2030 / 1 = 2030 (the remainder is 0, so 1 is a divisor of 2030)
2030 / 2 = 1015 (the remainder is 0, so 2 is a divisor of 2030)
2030 / 3 = 676.66666666667 (the remainder is 2, so 3 is not a divisor of 2030)
...
2030 / 2029 = 1.0004928536225 (the remainder is 1, so 2029 is not a divisor of 2030)
2030 / 2030 = 1 (the remainder is 0, so 2030 is a divisor of 2030)

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 2030 (i.e. 45.055521304275). 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 $\frac{N}{d} = D$ )

2030 / 1 = 2030 (the remainder is 0, so 1 and 2030 are divisors of 2030)
2030 / 2 = 1015 (the remainder is 0, so 2 and 1015 are divisors of 2030)
2030 / 3 = 676.66666666667 (the remainder is 2, so 3 is not a divisor of 2030)
...
2030 / 44 = 46.136363636364 (the remainder is 6, so 44 is not a divisor of 2030)
2030 / 45 = 45.111111111111 (the remainder is 5, so 45 is not a divisor of 2030)