What are the divisors of 4726?

1, 2, 17, 34, 139, 278, 2363, 4726

There is a total of 8 positive divisors.
The sum of these divisors is 7560.
The arithmetic mean is 945.

4 even divisors

2, 34, 278, 4726

4 odd divisors

1, 17, 139, 2363

How to compute the divisors of 4726?

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 4726 by each of the numbers from 1 to 4726 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)

4726 / 1 = 4726 (the remainder is 0, so 1 is a divisor of 4726)
4726 / 2 = 2363 (the remainder is 0, so 2 is a divisor of 4726)
4726 / 3 = 1575.3333333333 (the remainder is 1, so 3 is not a divisor of 4726)
...
4726 / 4725 = 1.0002116402116 (the remainder is 1, so 4725 is not a divisor of 4726)
4726 / 4726 = 1 (the remainder is 0, so 4726 is a divisor of 4726)

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 4726 (i.e. 68.745908969189). 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 $\frac{N}{d} = D$ )

4726 / 1 = 4726 (the remainder is 0, so 1 and 4726 are divisors of 4726)
4726 / 2 = 2363 (the remainder is 0, so 2 and 2363 are divisors of 4726)
4726 / 3 = 1575.3333333333 (the remainder is 1, so 3 is not a divisor of 4726)
...
4726 / 67 = 70.537313432836 (the remainder is 36, so 67 is not a divisor of 4726)
4726 / 68 = 69.5 (the remainder is 34, so 68 is not a divisor of 4726)