What are the divisors of 4767?

1, 3, 7, 21, 227, 681, 1589, 4767

There is a total of 8 positive divisors.
The sum of these divisors is 7296.
The arithmetic mean is 912.

8 odd divisors

1, 3, 7, 21, 227, 681, 1589, 4767

How to compute the divisors of 4767?

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 4767 by each of the numbers from 1 to 4767 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)

4767 / 1 = 4767 (the remainder is 0, so 1 is a divisor of 4767)
4767 / 2 = 2383.5 (the remainder is 1, so 2 is not a divisor of 4767)
4767 / 3 = 1589 (the remainder is 0, so 3 is a divisor of 4767)
...
4767 / 4766 = 1.0002098195552 (the remainder is 1, so 4766 is not a divisor of 4767)
4767 / 4767 = 1 (the remainder is 0, so 4767 is a divisor of 4767)

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 4767 (i.e. 69.043464571239). 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 $\frac{N}{d} = D$ )

4767 / 1 = 4767 (the remainder is 0, so 1 and 4767 are divisors of 4767)
4767 / 2 = 2383.5 (the remainder is 1, so 2 is not a divisor of 4767)
4767 / 3 = 1589 (the remainder is 0, so 3 and 1589 are divisors of 4767)
...
4767 / 68 = 70.102941176471 (the remainder is 7, so 68 is not a divisor of 4767)
4767 / 69 = 69.086956521739 (the remainder is 6, so 69 is not a divisor of 4767)