What are the divisors of 4816?

1, 2, 4, 7, 8, 14, 16, 28, 43, 56, 86, 112, 172, 301, 344, 602, 688, 1204, 2408, 4816

There is a total of 20 positive divisors.
The sum of these divisors is 10912.
The arithmetic mean is 545.6.

16 even divisors

2, 4, 8, 14, 16, 28, 56, 86, 112, 172, 344, 602, 688, 1204, 2408, 4816

4 odd divisors

1, 7, 43, 301

How to compute the divisors of 4816?

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 4816 by each of the numbers from 1 to 4816 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)

4816 / 1 = 4816 (the remainder is 0, so 1 is a divisor of 4816)
4816 / 2 = 2408 (the remainder is 0, so 2 is a divisor of 4816)
4816 / 3 = 1605.3333333333 (the remainder is 1, so 3 is not a divisor of 4816)
...
4816 / 4815 = 1.0002076843198 (the remainder is 1, so 4815 is not a divisor of 4816)
4816 / 4816 = 1 (the remainder is 0, so 4816 is a divisor of 4816)

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 4816 (i.e. 69.39740629159). 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 $\frac{N}{d} = D$ )

4816 / 1 = 4816 (the remainder is 0, so 1 and 4816 are divisors of 4816)
4816 / 2 = 2408 (the remainder is 0, so 2 and 2408 are divisors of 4816)
4816 / 3 = 1605.3333333333 (the remainder is 1, so 3 is not a divisor of 4816)
...
4816 / 68 = 70.823529411765 (the remainder is 56, so 68 is not a divisor of 4816)
4816 / 69 = 69.797101449275 (the remainder is 55, so 69 is not a divisor of 4816)