What are the divisors of 4649?

1, 4649

There is a total of 2 positive divisors.
The sum of these divisors is 4650.
The arithmetic mean is 2325.

2 odd divisors

1, 4649

How to compute the divisors of 4649?

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 4649 by each of the numbers from 1 to 4649 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)

4649 / 1 = 4649 (the remainder is 0, so 1 is a divisor of 4649)
4649 / 2 = 2324.5 (the remainder is 1, so 2 is not a divisor of 4649)
4649 / 3 = 1549.6666666667 (the remainder is 2, so 3 is not a divisor of 4649)
...
4649 / 4648 = 1.0002151462995 (the remainder is 1, so 4648 is not a divisor of 4649)
4649 / 4649 = 1 (the remainder is 0, so 4649 is a divisor of 4649)

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 4649 (i.e. 68.183575734923). 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 $\frac{N}{d} = D$ )

4649 / 1 = 4649 (the remainder is 0, so 1 and 4649 are divisors of 4649)
4649 / 2 = 2324.5 (the remainder is 1, so 2 is not a divisor of 4649)
4649 / 3 = 1549.6666666667 (the remainder is 2, so 3 is not a divisor of 4649)
...
4649 / 67 = 69.388059701493 (the remainder is 26, so 67 is not a divisor of 4649)
4649 / 68 = 68.367647058824 (the remainder is 25, so 68 is not a divisor of 4649)