What are the divisors of 4646?

1, 2, 23, 46, 101, 202, 2323, 4646

There is a total of 8 positive divisors.
The sum of these divisors is 7344.
The arithmetic mean is 918.

4 even divisors

2, 46, 202, 4646

4 odd divisors

1, 23, 101, 2323

How to compute the divisors of 4646?

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 4646 by each of the numbers from 1 to 4646 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)

4646 / 1 = 4646 (the remainder is 0, so 1 is a divisor of 4646)
4646 / 2 = 2323 (the remainder is 0, so 2 is a divisor of 4646)
4646 / 3 = 1548.6666666667 (the remainder is 2, so 3 is not a divisor of 4646)
...
4646 / 4645 = 1.000215285253 (the remainder is 1, so 4645 is not a divisor of 4646)
4646 / 4646 = 1 (the remainder is 0, so 4646 is a divisor of 4646)

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 4646 (i.e. 68.161572751808). 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 $\frac{N}{d} = D$ )

4646 / 1 = 4646 (the remainder is 0, so 1 and 4646 are divisors of 4646)
4646 / 2 = 2323 (the remainder is 0, so 2 and 2323 are divisors of 4646)
4646 / 3 = 1548.6666666667 (the remainder is 2, so 3 is not a divisor of 4646)
...
4646 / 67 = 69.34328358209 (the remainder is 23, so 67 is not a divisor of 4646)
4646 / 68 = 68.323529411765 (the remainder is 22, so 68 is not a divisor of 4646)