What are the divisors of 4761?

1, 3, 9, 23, 69, 207, 529, 1587, 4761

There is a total of 9 positive divisors.
The sum of these divisors is 7189.
The arithmetic mean is 798.77777777778.

9 odd divisors

1, 3, 9, 23, 69, 207, 529, 1587, 4761

How to compute the divisors of 4761?

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 4761 by each of the numbers from 1 to 4761 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)

4761 / 1 = 4761 (the remainder is 0, so 1 is a divisor of 4761)
4761 / 2 = 2380.5 (the remainder is 1, so 2 is not a divisor of 4761)
4761 / 3 = 1587 (the remainder is 0, so 3 is a divisor of 4761)
...
4761 / 4760 = 1.0002100840336 (the remainder is 1, so 4760 is not a divisor of 4761)
4761 / 4761 = 1 (the remainder is 0, so 4761 is a divisor of 4761)

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 4761 (i.e. 69). 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 $\frac{N}{d} = D$ )

4761 / 1 = 4761 (the remainder is 0, so 1 and 4761 are divisors of 4761)
4761 / 2 = 2380.5 (the remainder is 1, so 2 is not a divisor of 4761)
4761 / 3 = 1587 (the remainder is 0, so 3 and 1587 are divisors of 4761)
...
4761 / 68 = 70.014705882353 (the remainder is 1, so 68 is not a divisor of 4761)
4761 / 69 = 69 (the remainder is 0, so 69 and 69 are divisors of 4761)