What are the divisors of 4653?

1, 3, 9, 11, 33, 47, 99, 141, 423, 517, 1551, 4653

There is a total of 12 positive divisors.
The sum of these divisors is 7488.
The arithmetic mean is 624.

12 odd divisors

1, 3, 9, 11, 33, 47, 99, 141, 423, 517, 1551, 4653

How to compute the divisors of 4653?

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 4653 by each of the numbers from 1 to 4653 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)

4653 / 1 = 4653 (the remainder is 0, so 1 is a divisor of 4653)
4653 / 2 = 2326.5 (the remainder is 1, so 2 is not a divisor of 4653)
4653 / 3 = 1551 (the remainder is 0, so 3 is a divisor of 4653)
...
4653 / 4652 = 1.000214961307 (the remainder is 1, so 4652 is not a divisor of 4653)
4653 / 4653 = 1 (the remainder is 0, so 4653 is a divisor of 4653)

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 4653 (i.e. 68.212902005412). 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 $\frac{N}{d} = D$ )

4653 / 1 = 4653 (the remainder is 0, so 1 and 4653 are divisors of 4653)
4653 / 2 = 2326.5 (the remainder is 1, so 2 is not a divisor of 4653)
4653 / 3 = 1551 (the remainder is 0, so 3 and 1551 are divisors of 4653)
...
4653 / 67 = 69.44776119403 (the remainder is 30, so 67 is not a divisor of 4653)
4653 / 68 = 68.426470588235 (the remainder is 29, so 68 is not a divisor of 4653)