What are the divisors of 4753?

1, 7, 49, 97, 679, 4753

There is a total of 6 positive divisors.
The sum of these divisors is 5586.
The arithmetic mean is 931.

6 odd divisors

1, 7, 49, 97, 679, 4753

How to compute the divisors of 4753?

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 4753 by each of the numbers from 1 to 4753 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)

4753 / 1 = 4753 (the remainder is 0, so 1 is a divisor of 4753)
4753 / 2 = 2376.5 (the remainder is 1, so 2 is not a divisor of 4753)
4753 / 3 = 1584.3333333333 (the remainder is 1, so 3 is not a divisor of 4753)
...
4753 / 4752 = 1.0002104377104 (the remainder is 1, so 4752 is not a divisor of 4753)
4753 / 4753 = 1 (the remainder is 0, so 4753 is a divisor of 4753)

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 4753 (i.e. 68.942004612573). 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 $\frac{N}{d} = D$ )

4753 / 1 = 4753 (the remainder is 0, so 1 and 4753 are divisors of 4753)
4753 / 2 = 2376.5 (the remainder is 1, so 2 is not a divisor of 4753)
4753 / 3 = 1584.3333333333 (the remainder is 1, so 3 is not a divisor of 4753)
...
4753 / 67 = 70.940298507463 (the remainder is 63, so 67 is not a divisor of 4753)
4753 / 68 = 69.897058823529 (the remainder is 61, so 68 is not a divisor of 4753)