What are the divisors of 4481?

1, 4481

There is a total of 2 positive divisors.
The sum of these divisors is 4482.
The arithmetic mean is 2241.

2 odd divisors

1, 4481

How to compute the divisors of 4481?

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 4481 by each of the numbers from 1 to 4481 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)

4481 / 1 = 4481 (the remainder is 0, so 1 is a divisor of 4481)
4481 / 2 = 2240.5 (the remainder is 1, so 2 is not a divisor of 4481)
4481 / 3 = 1493.6666666667 (the remainder is 2, so 3 is not a divisor of 4481)
...
4481 / 4480 = 1.0002232142857 (the remainder is 1, so 4480 is not a divisor of 4481)
4481 / 4481 = 1 (the remainder is 0, so 4481 is a divisor of 4481)

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 4481 (i.e. 66.940271884718). 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 $\frac{N}{d} = D$ )

4481 / 1 = 4481 (the remainder is 0, so 1 and 4481 are divisors of 4481)
4481 / 2 = 2240.5 (the remainder is 1, so 2 is not a divisor of 4481)
4481 / 3 = 1493.6666666667 (the remainder is 2, so 3 is not a divisor of 4481)
...
4481 / 65 = 68.938461538462 (the remainder is 61, so 65 is not a divisor of 4481)
4481 / 66 = 67.893939393939 (the remainder is 59, so 66 is not a divisor of 4481)