What are the divisors of 4367?

1, 11, 397, 4367

There is a total of 4 positive divisors.
The sum of these divisors is 4776.
The arithmetic mean is 1194.

4 odd divisors

1, 11, 397, 4367

How to compute the divisors of 4367?

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 4367 by each of the numbers from 1 to 4367 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)

4367 / 1 = 4367 (the remainder is 0, so 1 is a divisor of 4367)
4367 / 2 = 2183.5 (the remainder is 1, so 2 is not a divisor of 4367)
4367 / 3 = 1455.6666666667 (the remainder is 2, so 3 is not a divisor of 4367)
...
4367 / 4366 = 1.0002290426019 (the remainder is 1, so 4366 is not a divisor of 4367)
4367 / 4367 = 1 (the remainder is 0, so 4367 is a divisor of 4367)

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 4367 (i.e. 66.083280790227). 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 $\frac{N}{d} = D$ )

4367 / 1 = 4367 (the remainder is 0, so 1 and 4367 are divisors of 4367)
4367 / 2 = 2183.5 (the remainder is 1, so 2 is not a divisor of 4367)
4367 / 3 = 1455.6666666667 (the remainder is 2, so 3 is not a divisor of 4367)
...
4367 / 65 = 67.184615384615 (the remainder is 12, so 65 is not a divisor of 4367)
4367 / 66 = 66.166666666667 (the remainder is 11, so 66 is not a divisor of 4367)