What are the divisors of 4397?

1, 4397

There is a total of 2 positive divisors.
The sum of these divisors is 4398.
The arithmetic mean is 2199.

2 odd divisors

1, 4397

How to compute the divisors of 4397?

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 4397 by each of the numbers from 1 to 4397 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)

4397 / 1 = 4397 (the remainder is 0, so 1 is a divisor of 4397)
4397 / 2 = 2198.5 (the remainder is 1, so 2 is not a divisor of 4397)
4397 / 3 = 1465.6666666667 (the remainder is 2, so 3 is not a divisor of 4397)
...
4397 / 4396 = 1.0002274795268 (the remainder is 1, so 4396 is not a divisor of 4397)
4397 / 4397 = 1 (the remainder is 0, so 4397 is a divisor of 4397)

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 4397 (i.e. 66.309878600402). 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 $\frac{N}{d} = D$ )

4397 / 1 = 4397 (the remainder is 0, so 1 and 4397 are divisors of 4397)
4397 / 2 = 2198.5 (the remainder is 1, so 2 is not a divisor of 4397)
4397 / 3 = 1465.6666666667 (the remainder is 2, so 3 is not a divisor of 4397)
...
4397 / 65 = 67.646153846154 (the remainder is 42, so 65 is not a divisor of 4397)
4397 / 66 = 66.621212121212 (the remainder is 41, so 66 is not a divisor of 4397)