What are the divisors of 2241?

1, 3, 9, 27, 83, 249, 747, 2241

There is a total of 8 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 420.

8 odd divisors

1, 3, 9, 27, 83, 249, 747, 2241

How to compute the divisors of 2241?

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 2241 by each of the numbers from 1 to 2241 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)

2241 / 1 = 2241 (the remainder is 0, so 1 is a divisor of 2241)
2241 / 2 = 1120.5 (the remainder is 1, so 2 is not a divisor of 2241)
2241 / 3 = 747 (the remainder is 0, so 3 is a divisor of 2241)
...
2241 / 2240 = 1.0004464285714 (the remainder is 1, so 2240 is not a divisor of 2241)
2241 / 2241 = 1 (the remainder is 0, so 2241 is a divisor of 2241)

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 2241 (i.e. 47.339201514178). 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 $\frac{N}{d} = D$ )

2241 / 1 = 2241 (the remainder is 0, so 1 and 2241 are divisors of 2241)
2241 / 2 = 1120.5 (the remainder is 1, so 2 is not a divisor of 2241)
2241 / 3 = 747 (the remainder is 0, so 3 and 747 are divisors of 2241)
...
2241 / 46 = 48.717391304348 (the remainder is 33, so 46 is not a divisor of 2241)
2241 / 47 = 47.68085106383 (the remainder is 32, so 47 is not a divisor of 2241)