What are the divisors of 4634?

1, 2, 7, 14, 331, 662, 2317, 4634

There is a total of 8 positive divisors.
The sum of these divisors is 7968.
The arithmetic mean is 996.

4 even divisors

2, 14, 662, 4634

4 odd divisors

1, 7, 331, 2317

How to compute the divisors of 4634?

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 4634 by each of the numbers from 1 to 4634 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)

4634 / 1 = 4634 (the remainder is 0, so 1 is a divisor of 4634)
4634 / 2 = 2317 (the remainder is 0, so 2 is a divisor of 4634)
4634 / 3 = 1544.6666666667 (the remainder is 2, so 3 is not a divisor of 4634)
...
4634 / 4633 = 1.0002158428664 (the remainder is 1, so 4633 is not a divisor of 4634)
4634 / 4634 = 1 (the remainder is 0, so 4634 is a divisor of 4634)

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 4634 (i.e. 68.07348970047). 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 $\frac{N}{d} = D$ )

4634 / 1 = 4634 (the remainder is 0, so 1 and 4634 are divisors of 4634)
4634 / 2 = 2317 (the remainder is 0, so 2 and 2317 are divisors of 4634)
4634 / 3 = 1544.6666666667 (the remainder is 2, so 3 is not a divisor of 4634)
...
4634 / 67 = 69.164179104478 (the remainder is 11, so 67 is not a divisor of 4634)
4634 / 68 = 68.147058823529 (the remainder is 10, so 68 is not a divisor of 4634)