What are the divisors of 4471?

1, 17, 263, 4471

There is a total of 4 positive divisors.
The sum of these divisors is 4752.
The arithmetic mean is 1188.

4 odd divisors

1, 17, 263, 4471

How to compute the divisors of 4471?

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 4471 by each of the numbers from 1 to 4471 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)

4471 / 1 = 4471 (the remainder is 0, so 1 is a divisor of 4471)
4471 / 2 = 2235.5 (the remainder is 1, so 2 is not a divisor of 4471)
4471 / 3 = 1490.3333333333 (the remainder is 1, so 3 is not a divisor of 4471)
...
4471 / 4470 = 1.0002237136465 (the remainder is 1, so 4470 is not a divisor of 4471)
4471 / 4471 = 1 (the remainder is 0, so 4471 is a divisor of 4471)

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 4471 (i.e. 66.865536713617). 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 $\frac{N}{d} = D$ )

4471 / 1 = 4471 (the remainder is 0, so 1 and 4471 are divisors of 4471)
4471 / 2 = 2235.5 (the remainder is 1, so 2 is not a divisor of 4471)
4471 / 3 = 1490.3333333333 (the remainder is 1, so 3 is not a divisor of 4471)
...
4471 / 65 = 68.784615384615 (the remainder is 51, so 65 is not a divisor of 4471)
4471 / 66 = 67.742424242424 (the remainder is 49, so 66 is not a divisor of 4471)