What are the divisors of 4783?

1, 4783

There is a total of 2 positive divisors.
The sum of these divisors is 4784.
The arithmetic mean is 2392.

2 odd divisors

1, 4783

How to compute the divisors of 4783?

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 4783 by each of the numbers from 1 to 4783 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)

4783 / 1 = 4783 (the remainder is 0, so 1 is a divisor of 4783)
4783 / 2 = 2391.5 (the remainder is 1, so 2 is not a divisor of 4783)
4783 / 3 = 1594.3333333333 (the remainder is 1, so 3 is not a divisor of 4783)
...
4783 / 4782 = 1.000209117524 (the remainder is 1, so 4782 is not a divisor of 4783)
4783 / 4783 = 1 (the remainder is 0, so 4783 is a divisor of 4783)

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 4783 (i.e. 69.159236548707). 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 $\frac{N}{d} = D$ )

4783 / 1 = 4783 (the remainder is 0, so 1 and 4783 are divisors of 4783)
4783 / 2 = 2391.5 (the remainder is 1, so 2 is not a divisor of 4783)
4783 / 3 = 1594.3333333333 (the remainder is 1, so 3 is not a divisor of 4783)
...
4783 / 68 = 70.338235294118 (the remainder is 23, so 68 is not a divisor of 4783)
4783 / 69 = 69.31884057971 (the remainder is 22, so 69 is not a divisor of 4783)