What are the divisors of 4706?

1, 2, 13, 26, 181, 362, 2353, 4706

There is a total of 8 positive divisors.
The sum of these divisors is 7644.
The arithmetic mean is 955.5.

4 even divisors

2, 26, 362, 4706

4 odd divisors

1, 13, 181, 2353

How to compute the divisors of 4706?

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 4706 by each of the numbers from 1 to 4706 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)

4706 / 1 = 4706 (the remainder is 0, so 1 is a divisor of 4706)
4706 / 2 = 2353 (the remainder is 0, so 2 is a divisor of 4706)
4706 / 3 = 1568.6666666667 (the remainder is 2, so 3 is not a divisor of 4706)
...
4706 / 4705 = 1.0002125398512 (the remainder is 1, so 4705 is not a divisor of 4706)
4706 / 4706 = 1 (the remainder is 0, so 4706 is a divisor of 4706)

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 4706 (i.e. 68.60029154457). 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 $\frac{N}{d} = D$ )

4706 / 1 = 4706 (the remainder is 0, so 1 and 4706 are divisors of 4706)
4706 / 2 = 2353 (the remainder is 0, so 2 and 2353 are divisors of 4706)
4706 / 3 = 1568.6666666667 (the remainder is 2, so 3 is not a divisor of 4706)
...
4706 / 67 = 70.238805970149 (the remainder is 16, so 67 is not a divisor of 4706)
4706 / 68 = 69.205882352941 (the remainder is 14, so 68 is not a divisor of 4706)