What are the divisors of 4510?

1, 2, 5, 10, 11, 22, 41, 55, 82, 110, 205, 410, 451, 902, 2255, 4510

There is a total of 16 positive divisors.
The sum of these divisors is 9072.
The arithmetic mean is 567.

8 even divisors

2, 10, 22, 82, 110, 410, 902, 4510

8 odd divisors

1, 5, 11, 41, 55, 205, 451, 2255

How to compute the divisors of 4510?

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 4510 by each of the numbers from 1 to 4510 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)

4510 / 1 = 4510 (the remainder is 0, so 1 is a divisor of 4510)
4510 / 2 = 2255 (the remainder is 0, so 2 is a divisor of 4510)
4510 / 3 = 1503.3333333333 (the remainder is 1, so 3 is not a divisor of 4510)
...
4510 / 4509 = 1.0002217786649 (the remainder is 1, so 4509 is not a divisor of 4510)
4510 / 4510 = 1 (the remainder is 0, so 4510 is a divisor of 4510)

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 4510 (i.e. 67.156533561523). 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 $\frac{N}{d} = D$ )

4510 / 1 = 4510 (the remainder is 0, so 1 and 4510 are divisors of 4510)
4510 / 2 = 2255 (the remainder is 0, so 2 and 2255 are divisors of 4510)
4510 / 3 = 1503.3333333333 (the remainder is 1, so 3 is not a divisor of 4510)
...
4510 / 66 = 68.333333333333 (the remainder is 22, so 66 is not a divisor of 4510)
4510 / 67 = 67.313432835821 (the remainder is 21, so 67 is not a divisor of 4510)