What are the divisors of 4301?

1, 11, 17, 23, 187, 253, 391, 4301

There is a total of 8 positive divisors.
The sum of these divisors is 5184.
The arithmetic mean is 648.

8 odd divisors

1, 11, 17, 23, 187, 253, 391, 4301

How to compute the divisors of 4301?

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 4301 by each of the numbers from 1 to 4301 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)

4301 / 1 = 4301 (the remainder is 0, so 1 is a divisor of 4301)
4301 / 2 = 2150.5 (the remainder is 1, so 2 is not a divisor of 4301)
4301 / 3 = 1433.6666666667 (the remainder is 2, so 3 is not a divisor of 4301)
...
4301 / 4300 = 1.0002325581395 (the remainder is 1, so 4300 is not a divisor of 4301)
4301 / 4301 = 1 (the remainder is 0, so 4301 is a divisor of 4301)

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 4301 (i.e. 65.582009728278). 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 $\frac{N}{d} = D$ )

4301 / 1 = 4301 (the remainder is 0, so 1 and 4301 are divisors of 4301)
4301 / 2 = 2150.5 (the remainder is 1, so 2 is not a divisor of 4301)
4301 / 3 = 1433.6666666667 (the remainder is 2, so 3 is not a divisor of 4301)
...
4301 / 64 = 67.203125 (the remainder is 13, so 64 is not a divisor of 4301)
4301 / 65 = 66.169230769231 (the remainder is 11, so 65 is not a divisor of 4301)