What are the divisors of 4431?

1, 3, 7, 21, 211, 633, 1477, 4431

There is a total of 8 positive divisors.
The sum of these divisors is 6784.
The arithmetic mean is 848.

8 odd divisors

1, 3, 7, 21, 211, 633, 1477, 4431

How to compute the divisors of 4431?

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 4431 by each of the numbers from 1 to 4431 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)

4431 / 1 = 4431 (the remainder is 0, so 1 is a divisor of 4431)
4431 / 2 = 2215.5 (the remainder is 1, so 2 is not a divisor of 4431)
4431 / 3 = 1477 (the remainder is 0, so 3 is a divisor of 4431)
...
4431 / 4430 = 1.0002257336343 (the remainder is 1, so 4430 is not a divisor of 4431)
4431 / 4431 = 1 (the remainder is 0, so 4431 is a divisor of 4431)

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 4431 (i.e. 66.56575696257). 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 $\frac{N}{d} = D$ )

4431 / 1 = 4431 (the remainder is 0, so 1 and 4431 are divisors of 4431)
4431 / 2 = 2215.5 (the remainder is 1, so 2 is not a divisor of 4431)
4431 / 3 = 1477 (the remainder is 0, so 3 and 1477 are divisors of 4431)
...
4431 / 65 = 68.169230769231 (the remainder is 11, so 65 is not a divisor of 4431)
4431 / 66 = 67.136363636364 (the remainder is 9, so 66 is not a divisor of 4431)