What are the divisors of 4796?

1, 2, 4, 11, 22, 44, 109, 218, 436, 1199, 2398, 4796

There is a total of 12 positive divisors.
The sum of these divisors is 9240.
The arithmetic mean is 770.

8 even divisors

2, 4, 22, 44, 218, 436, 2398, 4796

4 odd divisors

1, 11, 109, 1199

How to compute the divisors of 4796?

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 4796 by each of the numbers from 1 to 4796 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)

4796 / 1 = 4796 (the remainder is 0, so 1 is a divisor of 4796)
4796 / 2 = 2398 (the remainder is 0, so 2 is a divisor of 4796)
4796 / 3 = 1598.6666666667 (the remainder is 2, so 3 is not a divisor of 4796)
...
4796 / 4795 = 1.0002085505735 (the remainder is 1, so 4795 is not a divisor of 4796)
4796 / 4796 = 1 (the remainder is 0, so 4796 is a divisor of 4796)

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 4796 (i.e. 69.253158772723). 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 $\frac{N}{d} = D$ )

4796 / 1 = 4796 (the remainder is 0, so 1 and 4796 are divisors of 4796)
4796 / 2 = 2398 (the remainder is 0, so 2 and 2398 are divisors of 4796)
4796 / 3 = 1598.6666666667 (the remainder is 2, so 3 is not a divisor of 4796)
...
4796 / 68 = 70.529411764706 (the remainder is 36, so 68 is not a divisor of 4796)
4796 / 69 = 69.507246376812 (the remainder is 35, so 69 is not a divisor of 4796)