What are the divisors of 4696?

1, 2, 4, 8, 587, 1174, 2348, 4696

There is a total of 8 positive divisors.
The sum of these divisors is 8820.
The arithmetic mean is 1102.5.

6 even divisors

2, 4, 8, 1174, 2348, 4696

2 odd divisors

1, 587

How to compute the divisors of 4696?

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 4696 by each of the numbers from 1 to 4696 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)

4696 / 1 = 4696 (the remainder is 0, so 1 is a divisor of 4696)
4696 / 2 = 2348 (the remainder is 0, so 2 is a divisor of 4696)
4696 / 3 = 1565.3333333333 (the remainder is 1, so 3 is not a divisor of 4696)
...
4696 / 4695 = 1.0002129925453 (the remainder is 1, so 4695 is not a divisor of 4696)
4696 / 4696 = 1 (the remainder is 0, so 4696 is a divisor of 4696)

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 4696 (i.e. 68.527366796047). 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 $\frac{N}{d} = D$ )

4696 / 1 = 4696 (the remainder is 0, so 1 and 4696 are divisors of 4696)
4696 / 2 = 2348 (the remainder is 0, so 2 and 2348 are divisors of 4696)
4696 / 3 = 1565.3333333333 (the remainder is 1, so 3 is not a divisor of 4696)
...
4696 / 67 = 70.089552238806 (the remainder is 6, so 67 is not a divisor of 4696)
4696 / 68 = 69.058823529412 (the remainder is 4, so 68 is not a divisor of 4696)