What are the divisors of 4804?

1, 2, 4, 1201, 2402, 4804

There is a total of 6 positive divisors.
The sum of these divisors is 8414.
The arithmetic mean is 1402.3333333333.

4 even divisors

2, 4, 2402, 4804

2 odd divisors

1, 1201

How to compute the divisors of 4804?

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 4804 by each of the numbers from 1 to 4804 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)

4804 / 1 = 4804 (the remainder is 0, so 1 is a divisor of 4804)
4804 / 2 = 2402 (the remainder is 0, so 2 is a divisor of 4804)
4804 / 3 = 1601.3333333333 (the remainder is 1, so 3 is not a divisor of 4804)
...
4804 / 4803 = 1.0002082032063 (the remainder is 1, so 4803 is not a divisor of 4804)
4804 / 4804 = 1 (the remainder is 0, so 4804 is a divisor of 4804)

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 4804 (i.e. 69.310893804654). 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 $\frac{N}{d} = D$ )

4804 / 1 = 4804 (the remainder is 0, so 1 and 4804 are divisors of 4804)
4804 / 2 = 2402 (the remainder is 0, so 2 and 2402 are divisors of 4804)
4804 / 3 = 1601.3333333333 (the remainder is 1, so 3 is not a divisor of 4804)
...
4804 / 68 = 70.647058823529 (the remainder is 44, so 68 is not a divisor of 4804)
4804 / 69 = 69.623188405797 (the remainder is 43, so 69 is not a divisor of 4804)