What are the divisors of 4606?

1, 2, 7, 14, 47, 49, 94, 98, 329, 658, 2303, 4606

There is a total of 12 positive divisors.
The sum of these divisors is 8208.
The arithmetic mean is 684.

6 even divisors

2, 14, 94, 98, 658, 4606

6 odd divisors

1, 7, 47, 49, 329, 2303

How to compute the divisors of 4606?

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 4606 by each of the numbers from 1 to 4606 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)

4606 / 1 = 4606 (the remainder is 0, so 1 is a divisor of 4606)
4606 / 2 = 2303 (the remainder is 0, so 2 is a divisor of 4606)
4606 / 3 = 1535.3333333333 (the remainder is 1, so 3 is not a divisor of 4606)
...
4606 / 4605 = 1.000217155266 (the remainder is 1, so 4605 is not a divisor of 4606)
4606 / 4606 = 1 (the remainder is 0, so 4606 is a divisor of 4606)

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 4606 (i.e. 67.867518003829). 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 $\frac{N}{d} = D$ )

4606 / 1 = 4606 (the remainder is 0, so 1 and 4606 are divisors of 4606)
4606 / 2 = 2303 (the remainder is 0, so 2 and 2303 are divisors of 4606)
4606 / 3 = 1535.3333333333 (the remainder is 1, so 3 is not a divisor of 4606)
...
4606 / 66 = 69.787878787879 (the remainder is 52, so 66 is not a divisor of 4606)
4606 / 67 = 68.746268656716 (the remainder is 50, so 67 is not a divisor of 4606)