What are the divisors of 4506?

1, 2, 3, 6, 751, 1502, 2253, 4506

There is a total of 8 positive divisors.
The sum of these divisors is 9024.
The arithmetic mean is 1128.

4 even divisors

2, 6, 1502, 4506

4 odd divisors

1, 3, 751, 2253

How to compute the divisors of 4506?

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 4506 by each of the numbers from 1 to 4506 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)

4506 / 1 = 4506 (the remainder is 0, so 1 is a divisor of 4506)
4506 / 2 = 2253 (the remainder is 0, so 2 is a divisor of 4506)
4506 / 3 = 1502 (the remainder is 0, so 3 is a divisor of 4506)
...
4506 / 4505 = 1.0002219755827 (the remainder is 1, so 4505 is not a divisor of 4506)
4506 / 4506 = 1 (the remainder is 0, so 4506 is a divisor of 4506)

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 4506 (i.e. 67.126745787354). 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 $\frac{N}{d} = D$ )

4506 / 1 = 4506 (the remainder is 0, so 1 and 4506 are divisors of 4506)
4506 / 2 = 2253 (the remainder is 0, so 2 and 2253 are divisors of 4506)
4506 / 3 = 1502 (the remainder is 0, so 3 and 1502 are divisors of 4506)
...
4506 / 66 = 68.272727272727 (the remainder is 18, so 66 is not a divisor of 4506)
4506 / 67 = 67.253731343284 (the remainder is 17, so 67 is not a divisor of 4506)