What are the divisors of 4766?

1, 2, 2383, 4766

There is a total of 4 positive divisors.
The sum of these divisors is 7152.
The arithmetic mean is 1788.

2 even divisors

2, 4766

2 odd divisors

1, 2383

How to compute the divisors of 4766?

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 4766 by each of the numbers from 1 to 4766 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)

4766 / 1 = 4766 (the remainder is 0, so 1 is a divisor of 4766)
4766 / 2 = 2383 (the remainder is 0, so 2 is a divisor of 4766)
4766 / 3 = 1588.6666666667 (the remainder is 2, so 3 is not a divisor of 4766)
...
4766 / 4765 = 1.0002098635887 (the remainder is 1, so 4765 is not a divisor of 4766)
4766 / 4766 = 1 (the remainder is 0, so 4766 is a divisor of 4766)

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 4766 (i.e. 69.036222376373). 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 $\frac{N}{d} = D$ )

4766 / 1 = 4766 (the remainder is 0, so 1 and 4766 are divisors of 4766)
4766 / 2 = 2383 (the remainder is 0, so 2 and 2383 are divisors of 4766)
4766 / 3 = 1588.6666666667 (the remainder is 2, so 3 is not a divisor of 4766)
...
4766 / 68 = 70.088235294118 (the remainder is 6, so 68 is not a divisor of 4766)
4766 / 69 = 69.072463768116 (the remainder is 5, so 69 is not a divisor of 4766)