What are the divisors of 4786?

1, 2, 2393, 4786

There is a total of 4 positive divisors.
The sum of these divisors is 7182.
The arithmetic mean is 1795.5.

2 even divisors

2, 4786

2 odd divisors

1, 2393

How to compute the divisors of 4786?

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 4786 by each of the numbers from 1 to 4786 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)

4786 / 1 = 4786 (the remainder is 0, so 1 is a divisor of 4786)
4786 / 2 = 2393 (the remainder is 0, so 2 is a divisor of 4786)
4786 / 3 = 1595.3333333333 (the remainder is 1, so 3 is not a divisor of 4786)
...
4786 / 4785 = 1.0002089864159 (the remainder is 1, so 4785 is not a divisor of 4786)
4786 / 4786 = 1 (the remainder is 0, so 4786 is a divisor of 4786)

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 4786 (i.e. 69.180922225712). 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 $\frac{N}{d} = D$ )

4786 / 1 = 4786 (the remainder is 0, so 1 and 4786 are divisors of 4786)
4786 / 2 = 2393 (the remainder is 0, so 2 and 2393 are divisors of 4786)
4786 / 3 = 1595.3333333333 (the remainder is 1, so 3 is not a divisor of 4786)
...
4786 / 68 = 70.382352941176 (the remainder is 26, so 68 is not a divisor of 4786)
4786 / 69 = 69.36231884058 (the remainder is 25, so 69 is not a divisor of 4786)