What are the divisors of 4656?

1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 97, 194, 291, 388, 582, 776, 1164, 1552, 2328, 4656

There is a total of 20 positive divisors.
The sum of these divisors is 12152.
The arithmetic mean is 607.6.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 194, 388, 582, 776, 1164, 1552, 2328, 4656

4 odd divisors

1, 3, 97, 291

How to compute the divisors of 4656?

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 4656 by each of the numbers from 1 to 4656 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)

4656 / 1 = 4656 (the remainder is 0, so 1 is a divisor of 4656)
4656 / 2 = 2328 (the remainder is 0, so 2 is a divisor of 4656)
4656 / 3 = 1552 (the remainder is 0, so 3 is a divisor of 4656)
...
4656 / 4655 = 1.0002148227712 (the remainder is 1, so 4655 is not a divisor of 4656)
4656 / 4656 = 1 (the remainder is 0, so 4656 is a divisor of 4656)

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 4656 (i.e. 68.234888436928). 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 $\frac{N}{d} = D$ )

4656 / 1 = 4656 (the remainder is 0, so 1 and 4656 are divisors of 4656)
4656 / 2 = 2328 (the remainder is 0, so 2 and 2328 are divisors of 4656)
4656 / 3 = 1552 (the remainder is 0, so 3 and 1552 are divisors of 4656)
...
4656 / 67 = 69.492537313433 (the remainder is 33, so 67 is not a divisor of 4656)
4656 / 68 = 68.470588235294 (the remainder is 32, so 68 is not a divisor of 4656)