What are the divisors of 4399?

1, 53, 83, 4399

There is a total of 4 positive divisors.
The sum of these divisors is 4536.
The arithmetic mean is 1134.

4 odd divisors

1, 53, 83, 4399

How to compute the divisors of 4399?

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 4399 by each of the numbers from 1 to 4399 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)

4399 / 1 = 4399 (the remainder is 0, so 1 is a divisor of 4399)
4399 / 2 = 2199.5 (the remainder is 1, so 2 is not a divisor of 4399)
4399 / 3 = 1466.3333333333 (the remainder is 1, so 3 is not a divisor of 4399)
...
4399 / 4398 = 1.00022737608 (the remainder is 1, so 4398 is not a divisor of 4399)
4399 / 4399 = 1 (the remainder is 0, so 4399 is a divisor of 4399)

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 4399 (i.e. 66.324957595162). 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 $\frac{N}{d} = D$ )

4399 / 1 = 4399 (the remainder is 0, so 1 and 4399 are divisors of 4399)
4399 / 2 = 2199.5 (the remainder is 1, so 2 is not a divisor of 4399)
4399 / 3 = 1466.3333333333 (the remainder is 1, so 3 is not a divisor of 4399)
...
4399 / 65 = 67.676923076923 (the remainder is 44, so 65 is not a divisor of 4399)
4399 / 66 = 66.651515151515 (the remainder is 43, so 66 is not a divisor of 4399)