What are the divisors of 4633?

1, 41, 113, 4633

There is a total of 4 positive divisors.
The sum of these divisors is 4788.
The arithmetic mean is 1197.

4 odd divisors

1, 41, 113, 4633

How to compute the divisors of 4633?

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 4633 by each of the numbers from 1 to 4633 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)

4633 / 1 = 4633 (the remainder is 0, so 1 is a divisor of 4633)
4633 / 2 = 2316.5 (the remainder is 1, so 2 is not a divisor of 4633)
4633 / 3 = 1544.3333333333 (the remainder is 1, so 3 is not a divisor of 4633)
...
4633 / 4632 = 1.0002158894646 (the remainder is 1, so 4632 is not a divisor of 4633)
4633 / 4633 = 1 (the remainder is 0, so 4633 is a divisor of 4633)

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 4633 (i.e. 68.066144300967). 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 $\frac{N}{d} = D$ )

4633 / 1 = 4633 (the remainder is 0, so 1 and 4633 are divisors of 4633)
4633 / 2 = 2316.5 (the remainder is 1, so 2 is not a divisor of 4633)
4633 / 3 = 1544.3333333333 (the remainder is 1, so 3 is not a divisor of 4633)
...
4633 / 67 = 69.149253731343 (the remainder is 10, so 67 is not a divisor of 4633)
4633 / 68 = 68.132352941176 (the remainder is 9, so 68 is not a divisor of 4633)