What are the divisors of 4678?

1, 2, 2339, 4678

There is a total of 4 positive divisors.
The sum of these divisors is 7020.
The arithmetic mean is 1755.

2 even divisors

2, 4678

2 odd divisors

1, 2339

How to compute the divisors of 4678?

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 4678 by each of the numbers from 1 to 4678 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)

4678 / 1 = 4678 (the remainder is 0, so 1 is a divisor of 4678)
4678 / 2 = 2339 (the remainder is 0, so 2 is a divisor of 4678)
4678 / 3 = 1559.3333333333 (the remainder is 1, so 3 is not a divisor of 4678)
...
4678 / 4677 = 1.0002138122728 (the remainder is 1, so 4677 is not a divisor of 4678)
4678 / 4678 = 1 (the remainder is 0, so 4678 is a divisor of 4678)

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 4678 (i.e. 68.395906310246). 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 $\frac{N}{d} = D$ )

4678 / 1 = 4678 (the remainder is 0, so 1 and 4678 are divisors of 4678)
4678 / 2 = 2339 (the remainder is 0, so 2 and 2339 are divisors of 4678)
4678 / 3 = 1559.3333333333 (the remainder is 1, so 3 is not a divisor of 4678)
...
4678 / 67 = 69.820895522388 (the remainder is 55, so 67 is not a divisor of 4678)
4678 / 68 = 68.794117647059 (the remainder is 54, so 68 is not a divisor of 4678)