What are the divisors of 4793?

1, 4793

There is a total of 2 positive divisors.
The sum of these divisors is 4794.
The arithmetic mean is 2397.

2 odd divisors

1, 4793

How to compute the divisors of 4793?

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 4793 by each of the numbers from 1 to 4793 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)

4793 / 1 = 4793 (the remainder is 0, so 1 is a divisor of 4793)
4793 / 2 = 2396.5 (the remainder is 1, so 2 is not a divisor of 4793)
4793 / 3 = 1597.6666666667 (the remainder is 2, so 3 is not a divisor of 4793)
...
4793 / 4792 = 1.0002086811352 (the remainder is 1, so 4792 is not a divisor of 4793)
4793 / 4793 = 1 (the remainder is 0, so 4793 is a divisor of 4793)

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 4793 (i.e. 69.231495722684). 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 $\frac{N}{d} = D$ )

4793 / 1 = 4793 (the remainder is 0, so 1 and 4793 are divisors of 4793)
4793 / 2 = 2396.5 (the remainder is 1, so 2 is not a divisor of 4793)
4793 / 3 = 1597.6666666667 (the remainder is 2, so 3 is not a divisor of 4793)
...
4793 / 68 = 70.485294117647 (the remainder is 33, so 68 is not a divisor of 4793)
4793 / 69 = 69.463768115942 (the remainder is 32, so 69 is not a divisor of 4793)