What are the divisors of 4507?

1, 4507

There is a total of 2 positive divisors.
The sum of these divisors is 4508.
The arithmetic mean is 2254.

2 odd divisors

1, 4507

How to compute the divisors of 4507?

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 4507 by each of the numbers from 1 to 4507 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)

4507 / 1 = 4507 (the remainder is 0, so 1 is a divisor of 4507)
4507 / 2 = 2253.5 (the remainder is 1, so 2 is not a divisor of 4507)
4507 / 3 = 1502.3333333333 (the remainder is 1, so 3 is not a divisor of 4507)
...
4507 / 4506 = 1.0002219263205 (the remainder is 1, so 4506 is not a divisor of 4507)
4507 / 4507 = 1 (the remainder is 0, so 4507 is a divisor of 4507)

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 4507 (i.e. 67.134193969988). 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 $\frac{N}{d} = D$ )

4507 / 1 = 4507 (the remainder is 0, so 1 and 4507 are divisors of 4507)
4507 / 2 = 2253.5 (the remainder is 1, so 2 is not a divisor of 4507)
4507 / 3 = 1502.3333333333 (the remainder is 1, so 3 is not a divisor of 4507)
...
4507 / 66 = 68.287878787879 (the remainder is 19, so 66 is not a divisor of 4507)
4507 / 67 = 67.268656716418 (the remainder is 18, so 67 is not a divisor of 4507)