What are the divisors of 4441?

1, 4441

There is a total of 2 positive divisors.
The sum of these divisors is 4442.
The arithmetic mean is 2221.

2 odd divisors

1, 4441

How to compute the divisors of 4441?

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 4441 by each of the numbers from 1 to 4441 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)

4441 / 1 = 4441 (the remainder is 0, so 1 is a divisor of 4441)
4441 / 2 = 2220.5 (the remainder is 1, so 2 is not a divisor of 4441)
4441 / 3 = 1480.3333333333 (the remainder is 1, so 3 is not a divisor of 4441)
...
4441 / 4440 = 1.0002252252252 (the remainder is 1, so 4440 is not a divisor of 4441)
4441 / 4441 = 1 (the remainder is 0, so 4441 is a divisor of 4441)

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 4441 (i.e. 66.640828326185). 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 $\frac{N}{d} = D$ )

4441 / 1 = 4441 (the remainder is 0, so 1 and 4441 are divisors of 4441)
4441 / 2 = 2220.5 (the remainder is 1, so 2 is not a divisor of 4441)
4441 / 3 = 1480.3333333333 (the remainder is 1, so 3 is not a divisor of 4441)
...
4441 / 65 = 68.323076923077 (the remainder is 21, so 65 is not a divisor of 4441)
4441 / 66 = 67.287878787879 (the remainder is 19, so 66 is not a divisor of 4441)