What are the divisors of 4794?

1, 2, 3, 6, 17, 34, 47, 51, 94, 102, 141, 282, 799, 1598, 2397, 4794

There is a total of 16 positive divisors.
The sum of these divisors is 10368.
The arithmetic mean is 648.

8 even divisors

2, 6, 34, 94, 102, 282, 1598, 4794

8 odd divisors

1, 3, 17, 47, 51, 141, 799, 2397

How to compute the divisors of 4794?

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 4794 by each of the numbers from 1 to 4794 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)

4794 / 1 = 4794 (the remainder is 0, so 1 is a divisor of 4794)
4794 / 2 = 2397 (the remainder is 0, so 2 is a divisor of 4794)
4794 / 3 = 1598 (the remainder is 0, so 3 is a divisor of 4794)
...
4794 / 4793 = 1.0002086375965 (the remainder is 1, so 4793 is not a divisor of 4794)
4794 / 4794 = 1 (the remainder is 0, so 4794 is a divisor of 4794)

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 4794 (i.e. 69.238717492455). 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 $\frac{N}{d} = D$ )

4794 / 1 = 4794 (the remainder is 0, so 1 and 4794 are divisors of 4794)
4794 / 2 = 2397 (the remainder is 0, so 2 and 2397 are divisors of 4794)
4794 / 3 = 1598 (the remainder is 0, so 3 and 1598 are divisors of 4794)
...
4794 / 68 = 70.5 (the remainder is 34, so 68 is not a divisor of 4794)
4794 / 69 = 69.478260869565 (the remainder is 33, so 69 is not a divisor of 4794)