What are the divisors of 4479?

1, 3, 1493, 4479

There is a total of 4 positive divisors.
The sum of these divisors is 5976.
The arithmetic mean is 1494.

4 odd divisors

1, 3, 1493, 4479

How to compute the divisors of 4479?

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 4479 by each of the numbers from 1 to 4479 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)

4479 / 1 = 4479 (the remainder is 0, so 1 is a divisor of 4479)
4479 / 2 = 2239.5 (the remainder is 1, so 2 is not a divisor of 4479)
4479 / 3 = 1493 (the remainder is 0, so 3 is a divisor of 4479)
...
4479 / 4478 = 1.0002233139795 (the remainder is 1, so 4478 is not a divisor of 4479)
4479 / 4479 = 1 (the remainder is 0, so 4479 is a divisor of 4479)

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 4479 (i.e. 66.925331527009). 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 $\frac{N}{d} = D$ )

4479 / 1 = 4479 (the remainder is 0, so 1 and 4479 are divisors of 4479)
4479 / 2 = 2239.5 (the remainder is 1, so 2 is not a divisor of 4479)
4479 / 3 = 1493 (the remainder is 0, so 3 and 1493 are divisors of 4479)
...
4479 / 65 = 68.907692307692 (the remainder is 59, so 65 is not a divisor of 4479)
4479 / 66 = 67.863636363636 (the remainder is 57, so 66 is not a divisor of 4479)