What are the divisors of 4516?

1, 2, 4, 1129, 2258, 4516

There is a total of 6 positive divisors.
The sum of these divisors is 7910.
The arithmetic mean is 1318.3333333333.

4 even divisors

2, 4, 2258, 4516

2 odd divisors

1, 1129

How to compute the divisors of 4516?

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 4516 by each of the numbers from 1 to 4516 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)

4516 / 1 = 4516 (the remainder is 0, so 1 is a divisor of 4516)
4516 / 2 = 2258 (the remainder is 0, so 2 is a divisor of 4516)
4516 / 3 = 1505.3333333333 (the remainder is 1, so 3 is not a divisor of 4516)
...
4516 / 4515 = 1.0002214839424 (the remainder is 1, so 4515 is not a divisor of 4516)
4516 / 4516 = 1 (the remainder is 0, so 4516 is a divisor of 4516)

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 4516 (i.e. 67.201190465646). 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 $\frac{N}{d} = D$ )

4516 / 1 = 4516 (the remainder is 0, so 1 and 4516 are divisors of 4516)
4516 / 2 = 2258 (the remainder is 0, so 2 and 2258 are divisors of 4516)
4516 / 3 = 1505.3333333333 (the remainder is 1, so 3 is not a divisor of 4516)
...
4516 / 66 = 68.424242424242 (the remainder is 28, so 66 is not a divisor of 4516)
4516 / 67 = 67.402985074627 (the remainder is 27, so 67 is not a divisor of 4516)