What are the divisors of 4642?

1, 2, 11, 22, 211, 422, 2321, 4642

There is a total of 8 positive divisors.
The sum of these divisors is 7632.
The arithmetic mean is 954.

4 even divisors

2, 22, 422, 4642

4 odd divisors

1, 11, 211, 2321

How to compute the divisors of 4642?

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 4642 by each of the numbers from 1 to 4642 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)

4642 / 1 = 4642 (the remainder is 0, so 1 is a divisor of 4642)
4642 / 2 = 2321 (the remainder is 0, so 2 is a divisor of 4642)
4642 / 3 = 1547.3333333333 (the remainder is 1, so 3 is not a divisor of 4642)
...
4642 / 4641 = 1.0002154708037 (the remainder is 1, so 4641 is not a divisor of 4642)
4642 / 4642 = 1 (the remainder is 0, so 4642 is a divisor of 4642)

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 4642 (i.e. 68.132224387583). 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 $\frac{N}{d} = D$ )

4642 / 1 = 4642 (the remainder is 0, so 1 and 4642 are divisors of 4642)
4642 / 2 = 2321 (the remainder is 0, so 2 and 2321 are divisors of 4642)
4642 / 3 = 1547.3333333333 (the remainder is 1, so 3 is not a divisor of 4642)
...
4642 / 67 = 69.283582089552 (the remainder is 19, so 67 is not a divisor of 4642)
4642 / 68 = 68.264705882353 (the remainder is 18, so 68 is not a divisor of 4642)