What are the divisors of 4529?

1, 7, 647, 4529

There is a total of 4 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 1296.

4 odd divisors

1, 7, 647, 4529

How to compute the divisors of 4529?

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 4529 by each of the numbers from 1 to 4529 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)

4529 / 1 = 4529 (the remainder is 0, so 1 is a divisor of 4529)
4529 / 2 = 2264.5 (the remainder is 1, so 2 is not a divisor of 4529)
4529 / 3 = 1509.6666666667 (the remainder is 2, so 3 is not a divisor of 4529)
...
4529 / 4528 = 1.0002208480565 (the remainder is 1, so 4528 is not a divisor of 4529)
4529 / 4529 = 1 (the remainder is 0, so 4529 is a divisor of 4529)

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 4529 (i.e. 67.297845433565). 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 $\frac{N}{d} = D$ )

4529 / 1 = 4529 (the remainder is 0, so 1 and 4529 are divisors of 4529)
4529 / 2 = 2264.5 (the remainder is 1, so 2 is not a divisor of 4529)
4529 / 3 = 1509.6666666667 (the remainder is 2, so 3 is not a divisor of 4529)
...
4529 / 66 = 68.621212121212 (the remainder is 41, so 66 is not a divisor of 4529)
4529 / 67 = 67.597014925373 (the remainder is 40, so 67 is not a divisor of 4529)