What are the divisors of 4704?

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 49, 56, 84, 96, 98, 112, 147, 168, 196, 224, 294, 336, 392, 588, 672, 784, 1176, 1568, 2352, 4704

There is a total of 36 positive divisors.
The sum of these divisors is 14364.
The arithmetic mean is 399.

30 even divisors

2, 4, 6, 8, 12, 14, 16, 24, 28, 32, 42, 48, 56, 84, 96, 98, 112, 168, 196, 224, 294, 336, 392, 588, 672, 784, 1176, 1568, 2352, 4704

6 odd divisors

1, 3, 7, 21, 49, 147

How to compute the divisors of 4704?

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 4704 by each of the numbers from 1 to 4704 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)

4704 / 1 = 4704 (the remainder is 0, so 1 is a divisor of 4704)
4704 / 2 = 2352 (the remainder is 0, so 2 is a divisor of 4704)
4704 / 3 = 1568 (the remainder is 0, so 3 is a divisor of 4704)
...
4704 / 4703 = 1.000212630236 (the remainder is 1, so 4703 is not a divisor of 4704)
4704 / 4704 = 1 (the remainder is 0, so 4704 is a divisor of 4704)

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 4704 (i.e. 68.585712797929). 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 $\frac{N}{d} = D$ )

4704 / 1 = 4704 (the remainder is 0, so 1 and 4704 are divisors of 4704)
4704 / 2 = 2352 (the remainder is 0, so 2 and 2352 are divisors of 4704)
4704 / 3 = 1568 (the remainder is 0, so 3 and 1568 are divisors of 4704)
...
4704 / 67 = 70.208955223881 (the remainder is 14, so 67 is not a divisor of 4704)
4704 / 68 = 69.176470588235 (the remainder is 12, so 68 is not a divisor of 4704)