What are the divisors of 4527?

1, 3, 9, 503, 1509, 4527

There is a total of 6 positive divisors.
The sum of these divisors is 6552.
The arithmetic mean is 1092.

6 odd divisors

1, 3, 9, 503, 1509, 4527

How to compute the divisors of 4527?

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 4527 by each of the numbers from 1 to 4527 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)

4527 / 1 = 4527 (the remainder is 0, so 1 is a divisor of 4527)
4527 / 2 = 2263.5 (the remainder is 1, so 2 is not a divisor of 4527)
4527 / 3 = 1509 (the remainder is 0, so 3 is a divisor of 4527)
...
4527 / 4526 = 1.0002209456474 (the remainder is 1, so 4526 is not a divisor of 4527)
4527 / 4527 = 1 (the remainder is 0, so 4527 is a divisor of 4527)

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 4527 (i.e. 67.282984476017). 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 $\frac{N}{d} = D$ )

4527 / 1 = 4527 (the remainder is 0, so 1 and 4527 are divisors of 4527)
4527 / 2 = 2263.5 (the remainder is 1, so 2 is not a divisor of 4527)
4527 / 3 = 1509 (the remainder is 0, so 3 and 1509 are divisors of 4527)
...
4527 / 66 = 68.590909090909 (the remainder is 39, so 66 is not a divisor of 4527)
4527 / 67 = 67.567164179104 (the remainder is 38, so 67 is not a divisor of 4527)