What are the divisors of 4659?

1, 3, 1553, 4659

There is a total of 4 positive divisors.
The sum of these divisors is 6216.
The arithmetic mean is 1554.

4 odd divisors

1, 3, 1553, 4659

How to compute the divisors of 4659?

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 4659 by each of the numbers from 1 to 4659 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)

4659 / 1 = 4659 (the remainder is 0, so 1 is a divisor of 4659)
4659 / 2 = 2329.5 (the remainder is 1, so 2 is not a divisor of 4659)
4659 / 3 = 1553 (the remainder is 0, so 3 is a divisor of 4659)
...
4659 / 4658 = 1.0002146844139 (the remainder is 1, so 4658 is not a divisor of 4659)
4659 / 4659 = 1 (the remainder is 0, so 4659 is a divisor of 4659)

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 4659 (i.e. 68.256867786326). 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 $\frac{N}{d} = D$ )

4659 / 1 = 4659 (the remainder is 0, so 1 and 4659 are divisors of 4659)
4659 / 2 = 2329.5 (the remainder is 1, so 2 is not a divisor of 4659)
4659 / 3 = 1553 (the remainder is 0, so 3 and 1553 are divisors of 4659)
...
4659 / 67 = 69.537313432836 (the remainder is 36, so 67 is not a divisor of 4659)
4659 / 68 = 68.514705882353 (the remainder is 35, so 68 is not a divisor of 4659)