What are the divisors of 4073?

1, 4073

There is a total of 2 positive divisors.
The sum of these divisors is 4074.
The arithmetic mean is 2037.

2 odd divisors

1, 4073

How to compute the divisors of 4073?

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 4073 by each of the numbers from 1 to 4073 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)

4073 / 1 = 4073 (the remainder is 0, so 1 is a divisor of 4073)
4073 / 2 = 2036.5 (the remainder is 1, so 2 is not a divisor of 4073)
4073 / 3 = 1357.6666666667 (the remainder is 2, so 3 is not a divisor of 4073)
...
4073 / 4072 = 1.0002455795678 (the remainder is 1, so 4072 is not a divisor of 4073)
4073 / 4073 = 1 (the remainder is 0, so 4073 is a divisor of 4073)

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 4073 (i.e. 63.820059542435). 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 $\frac{N}{d} = D$ )

4073 / 1 = 4073 (the remainder is 0, so 1 and 4073 are divisors of 4073)
4073 / 2 = 2036.5 (the remainder is 1, so 2 is not a divisor of 4073)
4073 / 3 = 1357.6666666667 (the remainder is 2, so 3 is not a divisor of 4073)
...
4073 / 62 = 65.693548387097 (the remainder is 43, so 62 is not a divisor of 4073)
4073 / 63 = 64.650793650794 (the remainder is 41, so 63 is not a divisor of 4073)