What are the divisors of 4773?

1, 3, 37, 43, 111, 129, 1591, 4773

There is a total of 8 positive divisors.
The sum of these divisors is 6688.
The arithmetic mean is 836.

8 odd divisors

1, 3, 37, 43, 111, 129, 1591, 4773

How to compute the divisors of 4773?

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 4773 by each of the numbers from 1 to 4773 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)

4773 / 1 = 4773 (the remainder is 0, so 1 is a divisor of 4773)
4773 / 2 = 2386.5 (the remainder is 1, so 2 is not a divisor of 4773)
4773 / 3 = 1591 (the remainder is 0, so 3 is a divisor of 4773)
...
4773 / 4772 = 1.0002095557418 (the remainder is 1, so 4772 is not a divisor of 4773)
4773 / 4773 = 1 (the remainder is 0, so 4773 is a divisor of 4773)

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 4773 (i.e. 69.086901797664). 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 $\frac{N}{d} = D$ )

4773 / 1 = 4773 (the remainder is 0, so 1 and 4773 are divisors of 4773)
4773 / 2 = 2386.5 (the remainder is 1, so 2 is not a divisor of 4773)
4773 / 3 = 1591 (the remainder is 0, so 3 and 1591 are divisors of 4773)
...
4773 / 68 = 70.191176470588 (the remainder is 13, so 68 is not a divisor of 4773)
4773 / 69 = 69.173913043478 (the remainder is 12, so 69 is not a divisor of 4773)