What are the divisors of 4388?

1, 2, 4, 1097, 2194, 4388

There is a total of 6 positive divisors.
The sum of these divisors is 7686.
The arithmetic mean is 1281.

4 even divisors

2, 4, 2194, 4388

2 odd divisors

1, 1097

How to compute the divisors of 4388?

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 4388 by each of the numbers from 1 to 4388 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)

4388 / 1 = 4388 (the remainder is 0, so 1 is a divisor of 4388)
4388 / 2 = 2194 (the remainder is 0, so 2 is a divisor of 4388)
4388 / 3 = 1462.6666666667 (the remainder is 2, so 3 is not a divisor of 4388)
...
4388 / 4387 = 1.0002279462047 (the remainder is 1, so 4387 is not a divisor of 4388)
4388 / 4388 = 1 (the remainder is 0, so 4388 is a divisor of 4388)

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 4388 (i.e. 66.241980646717). 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 $\frac{N}{d} = D$ )

4388 / 1 = 4388 (the remainder is 0, so 1 and 4388 are divisors of 4388)
4388 / 2 = 2194 (the remainder is 0, so 2 and 2194 are divisors of 4388)
4388 / 3 = 1462.6666666667 (the remainder is 2, so 3 is not a divisor of 4388)
...
4388 / 65 = 67.507692307692 (the remainder is 33, so 65 is not a divisor of 4388)
4388 / 66 = 66.484848484848 (the remainder is 32, so 66 is not a divisor of 4388)