What are the divisors of 4657?

1, 4657

There is a total of 2 positive divisors.
The sum of these divisors is 4658.
The arithmetic mean is 2329.

2 odd divisors

1, 4657

How to compute the divisors of 4657?

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 4657 by each of the numbers from 1 to 4657 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)

4657 / 1 = 4657 (the remainder is 0, so 1 is a divisor of 4657)
4657 / 2 = 2328.5 (the remainder is 1, so 2 is not a divisor of 4657)
4657 / 3 = 1552.3333333333 (the remainder is 1, so 3 is not a divisor of 4657)
...
4657 / 4656 = 1.0002147766323 (the remainder is 1, so 4656 is not a divisor of 4657)
4657 / 4657 = 1 (the remainder is 0, so 4657 is a divisor of 4657)

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 4657 (i.e. 68.242215673291). 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 $\frac{N}{d} = D$ )

4657 / 1 = 4657 (the remainder is 0, so 1 and 4657 are divisors of 4657)
4657 / 2 = 2328.5 (the remainder is 1, so 2 is not a divisor of 4657)
4657 / 3 = 1552.3333333333 (the remainder is 1, so 3 is not a divisor of 4657)
...
4657 / 67 = 69.507462686567 (the remainder is 34, so 67 is not a divisor of 4657)
4657 / 68 = 68.485294117647 (the remainder is 33, so 68 is not a divisor of 4657)