What are the divisors of 4864?

1, 2, 4, 8, 16, 19, 32, 38, 64, 76, 128, 152, 256, 304, 608, 1216, 2432, 4864

There is a total of 18 positive divisors.
The sum of these divisors is 10220.
The arithmetic mean is 567.77777777778.

16 even divisors

2, 4, 8, 16, 32, 38, 64, 76, 128, 152, 256, 304, 608, 1216, 2432, 4864

2 odd divisors

1, 19

How to compute the divisors of 4864?

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 4864 by each of the numbers from 1 to 4864 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)

4864 / 1 = 4864 (the remainder is 0, so 1 is a divisor of 4864)
4864 / 2 = 2432 (the remainder is 0, so 2 is a divisor of 4864)
4864 / 3 = 1621.3333333333 (the remainder is 1, so 3 is not a divisor of 4864)
...
4864 / 4863 = 1.0002056343821 (the remainder is 1, so 4863 is not a divisor of 4864)
4864 / 4864 = 1 (the remainder is 0, so 4864 is a divisor of 4864)

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 4864 (i.e. 69.742383096651). 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 $\frac{N}{d} = D$ )

4864 / 1 = 4864 (the remainder is 0, so 1 and 4864 are divisors of 4864)
4864 / 2 = 2432 (the remainder is 0, so 2 and 2432 are divisors of 4864)
4864 / 3 = 1621.3333333333 (the remainder is 1, so 3 is not a divisor of 4864)
...
4864 / 68 = 71.529411764706 (the remainder is 36, so 68 is not a divisor of 4864)
4864 / 69 = 70.492753623188 (the remainder is 34, so 69 is not a divisor of 4864)