What are the divisors of 4311?

1, 3, 9, 479, 1437, 4311

There is a total of 6 positive divisors.
The sum of these divisors is 6240.
The arithmetic mean is 1040.

6 odd divisors

1, 3, 9, 479, 1437, 4311

How to compute the divisors of 4311?

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 4311 by each of the numbers from 1 to 4311 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)

4311 / 1 = 4311 (the remainder is 0, so 1 is a divisor of 4311)
4311 / 2 = 2155.5 (the remainder is 1, so 2 is not a divisor of 4311)
4311 / 3 = 1437 (the remainder is 0, so 3 is a divisor of 4311)
...
4311 / 4310 = 1.0002320185615 (the remainder is 1, so 4310 is not a divisor of 4311)
4311 / 4311 = 1 (the remainder is 0, so 4311 is a divisor of 4311)

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 4311 (i.e. 65.658205884718). 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 $\frac{N}{d} = D$ )

4311 / 1 = 4311 (the remainder is 0, so 1 and 4311 are divisors of 4311)
4311 / 2 = 2155.5 (the remainder is 1, so 2 is not a divisor of 4311)
4311 / 3 = 1437 (the remainder is 0, so 3 and 1437 are divisors of 4311)
...
4311 / 64 = 67.359375 (the remainder is 23, so 64 is not a divisor of 4311)
4311 / 65 = 66.323076923077 (the remainder is 21, so 65 is not a divisor of 4311)