What are the divisors of 4759?

1, 4759

There is a total of 2 positive divisors.
The sum of these divisors is 4760.
The arithmetic mean is 2380.

2 odd divisors

1, 4759

How to compute the divisors of 4759?

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 4759 by each of the numbers from 1 to 4759 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)

4759 / 1 = 4759 (the remainder is 0, so 1 is a divisor of 4759)
4759 / 2 = 2379.5 (the remainder is 1, so 2 is not a divisor of 4759)
4759 / 3 = 1586.3333333333 (the remainder is 1, so 3 is not a divisor of 4759)
...
4759 / 4758 = 1.0002101723413 (the remainder is 1, so 4758 is not a divisor of 4759)
4759 / 4759 = 1 (the remainder is 0, so 4759 is a divisor of 4759)

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 4759 (i.e. 68.985505724029). 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 $\frac{N}{d} = D$ )

4759 / 1 = 4759 (the remainder is 0, so 1 and 4759 are divisors of 4759)
4759 / 2 = 2379.5 (the remainder is 1, so 2 is not a divisor of 4759)
4759 / 3 = 1586.3333333333 (the remainder is 1, so 3 is not a divisor of 4759)
...
4759 / 67 = 71.029850746269 (the remainder is 2, so 67 is not a divisor of 4759)
4759 / 68 = 69.985294117647 (the remainder is 67, so 68 is not a divisor of 4759)