What are the divisors of 4792?

1, 2, 4, 8, 599, 1198, 2396, 4792

There is a total of 8 positive divisors.
The sum of these divisors is 9000.
The arithmetic mean is 1125.

6 even divisors

2, 4, 8, 1198, 2396, 4792

2 odd divisors

1, 599

How to compute the divisors of 4792?

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 4792 by each of the numbers from 1 to 4792 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)

4792 / 1 = 4792 (the remainder is 0, so 1 is a divisor of 4792)
4792 / 2 = 2396 (the remainder is 0, so 2 is a divisor of 4792)
4792 / 3 = 1597.3333333333 (the remainder is 1, so 3 is not a divisor of 4792)
...
4792 / 4791 = 1.0002087246921 (the remainder is 1, so 4791 is not a divisor of 4792)
4792 / 4792 = 1 (the remainder is 0, so 4792 is a divisor of 4792)

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 4792 (i.e. 69.224273199507). 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 $\frac{N}{d} = D$ )

4792 / 1 = 4792 (the remainder is 0, so 1 and 4792 are divisors of 4792)
4792 / 2 = 2396 (the remainder is 0, so 2 and 2396 are divisors of 4792)
4792 / 3 = 1597.3333333333 (the remainder is 1, so 3 is not a divisor of 4792)
...
4792 / 68 = 70.470588235294 (the remainder is 32, so 68 is not a divisor of 4792)
4792 / 69 = 69.449275362319 (the remainder is 31, so 69 is not a divisor of 4792)