What are the divisors of 4521?

1, 3, 11, 33, 137, 411, 1507, 4521

There is a total of 8 positive divisors.
The sum of these divisors is 6624.
The arithmetic mean is 828.

8 odd divisors

1, 3, 11, 33, 137, 411, 1507, 4521

How to compute the divisors of 4521?

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 4521 by each of the numbers from 1 to 4521 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)

4521 / 1 = 4521 (the remainder is 0, so 1 is a divisor of 4521)
4521 / 2 = 2260.5 (the remainder is 1, so 2 is not a divisor of 4521)
4521 / 3 = 1507 (the remainder is 0, so 3 is a divisor of 4521)
...
4521 / 4520 = 1.0002212389381 (the remainder is 1, so 4520 is not a divisor of 4521)
4521 / 4521 = 1 (the remainder is 0, so 4521 is a divisor of 4521)

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 4521 (i.e. 67.238381896057). 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 $\frac{N}{d} = D$ )

4521 / 1 = 4521 (the remainder is 0, so 1 and 4521 are divisors of 4521)
4521 / 2 = 2260.5 (the remainder is 1, so 2 is not a divisor of 4521)
4521 / 3 = 1507 (the remainder is 0, so 3 and 1507 are divisors of 4521)
...
4521 / 66 = 68.5 (the remainder is 33, so 66 is not a divisor of 4521)
4521 / 67 = 67.477611940299 (the remainder is 32, so 67 is not a divisor of 4521)