What are the divisors of 4478?

1, 2, 2239, 4478

There is a total of 4 positive divisors.
The sum of these divisors is 6720.
The arithmetic mean is 1680.

2 even divisors

2, 4478

2 odd divisors

1, 2239

How to compute the divisors of 4478?

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 4478 by each of the numbers from 1 to 4478 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)

4478 / 1 = 4478 (the remainder is 0, so 1 is a divisor of 4478)
4478 / 2 = 2239 (the remainder is 0, so 2 is a divisor of 4478)
4478 / 3 = 1492.6666666667 (the remainder is 2, so 3 is not a divisor of 4478)
...
4478 / 4477 = 1.0002233638597 (the remainder is 1, so 4477 is not a divisor of 4478)
4478 / 4478 = 1 (the remainder is 0, so 4478 is a divisor of 4478)

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 4478 (i.e. 66.917860097286). 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 $\frac{N}{d} = D$ )

4478 / 1 = 4478 (the remainder is 0, so 1 and 4478 are divisors of 4478)
4478 / 2 = 2239 (the remainder is 0, so 2 and 2239 are divisors of 4478)
4478 / 3 = 1492.6666666667 (the remainder is 2, so 3 is not a divisor of 4478)
...
4478 / 65 = 68.892307692308 (the remainder is 58, so 65 is not a divisor of 4478)
4478 / 66 = 67.848484848485 (the remainder is 56, so 66 is not a divisor of 4478)