What are the divisors of 4390?

1, 2, 5, 10, 439, 878, 2195, 4390

There is a total of 8 positive divisors.
The sum of these divisors is 7920.
The arithmetic mean is 990.

4 even divisors

2, 10, 878, 4390

4 odd divisors

1, 5, 439, 2195

How to compute the divisors of 4390?

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 4390 by each of the numbers from 1 to 4390 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)

4390 / 1 = 4390 (the remainder is 0, so 1 is a divisor of 4390)
4390 / 2 = 2195 (the remainder is 0, so 2 is a divisor of 4390)
4390 / 3 = 1463.3333333333 (the remainder is 1, so 3 is not a divisor of 4390)
...
4390 / 4389 = 1.0002278423331 (the remainder is 1, so 4389 is not a divisor of 4390)
4390 / 4390 = 1 (the remainder is 0, so 4390 is a divisor of 4390)

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 4390 (i.e. 66.25707509391). 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 $\frac{N}{d} = D$ )

4390 / 1 = 4390 (the remainder is 0, so 1 and 4390 are divisors of 4390)
4390 / 2 = 2195 (the remainder is 0, so 2 and 2195 are divisors of 4390)
4390 / 3 = 1463.3333333333 (the remainder is 1, so 3 is not a divisor of 4390)
...
4390 / 65 = 67.538461538462 (the remainder is 35, so 65 is not a divisor of 4390)
4390 / 66 = 66.515151515152 (the remainder is 34, so 66 is not a divisor of 4390)