What are the divisors of 4896?

1, 2, 3, 4, 6, 8, 9, 12, 16, 17, 18, 24, 32, 34, 36, 48, 51, 68, 72, 96, 102, 136, 144, 153, 204, 272, 288, 306, 408, 544, 612, 816, 1224, 1632, 2448, 4896

There is a total of 36 positive divisors.
The sum of these divisors is 14742.
The arithmetic mean is 409.5.

30 even divisors

2, 4, 6, 8, 12, 16, 18, 24, 32, 34, 36, 48, 68, 72, 96, 102, 136, 144, 204, 272, 288, 306, 408, 544, 612, 816, 1224, 1632, 2448, 4896

6 odd divisors

1, 3, 9, 17, 51, 153

How to compute the divisors of 4896?

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 4896 by each of the numbers from 1 to 4896 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)

4896 / 1 = 4896 (the remainder is 0, so 1 is a divisor of 4896)
4896 / 2 = 2448 (the remainder is 0, so 2 is a divisor of 4896)
4896 / 3 = 1632 (the remainder is 0, so 3 is a divisor of 4896)
...
4896 / 4895 = 1.0002042900919 (the remainder is 1, so 4895 is not a divisor of 4896)
4896 / 4896 = 1 (the remainder is 0, so 4896 is a divisor of 4896)

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 4896 (i.e. 69.971422738144). 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 $\frac{N}{d} = D$ )

4896 / 1 = 4896 (the remainder is 0, so 1 and 4896 are divisors of 4896)
4896 / 2 = 2448 (the remainder is 0, so 2 and 2448 are divisors of 4896)
4896 / 3 = 1632 (the remainder is 0, so 3 and 1632 are divisors of 4896)
...
4896 / 68 = 72 (the remainder is 0, so 68 and 72 are divisors of 4896)
4896 / 69 = 70.95652173913 (the remainder is 66, so 69 is not a divisor of 4896)