What are the divisors of 2073?

1, 3, 691, 2073

There is a total of 4 positive divisors.
The sum of these divisors is 2768.
The arithmetic mean is 692.

4 odd divisors

1, 3, 691, 2073

How to compute the divisors of 2073?

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 2073 by each of the numbers from 1 to 2073 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)

2073 / 1 = 2073 (the remainder is 0, so 1 is a divisor of 2073)
2073 / 2 = 1036.5 (the remainder is 1, so 2 is not a divisor of 2073)
2073 / 3 = 691 (the remainder is 0, so 3 is a divisor of 2073)
...
2073 / 2072 = 1.0004826254826 (the remainder is 1, so 2072 is not a divisor of 2073)
2073 / 2073 = 1 (the remainder is 0, so 2073 is a divisor of 2073)

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 2073 (i.e. 45.530209751329). 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 $\frac{N}{d} = D$ )

2073 / 1 = 2073 (the remainder is 0, so 1 and 2073 are divisors of 2073)
2073 / 2 = 1036.5 (the remainder is 1, so 2 is not a divisor of 2073)
2073 / 3 = 691 (the remainder is 0, so 3 and 691 are divisors of 2073)
...
2073 / 44 = 47.113636363636 (the remainder is 5, so 44 is not a divisor of 2073)
2073 / 45 = 46.066666666667 (the remainder is 3, so 45 is not a divisor of 2073)