What are the divisors of 1281?

1, 3, 7, 21, 61, 183, 427, 1281

There is a total of 8 positive divisors.
The sum of these divisors is 1984.
The arithmetic mean is 248.

8 odd divisors

1, 3, 7, 21, 61, 183, 427, 1281

How to compute the divisors of 1281?

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 1281 by each of the numbers from 1 to 1281 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)

1281 / 1 = 1281 (the remainder is 0, so 1 is a divisor of 1281)
1281 / 2 = 640.5 (the remainder is 1, so 2 is not a divisor of 1281)
1281 / 3 = 427 (the remainder is 0, so 3 is a divisor of 1281)
...
1281 / 1280 = 1.00078125 (the remainder is 1, so 1280 is not a divisor of 1281)
1281 / 1281 = 1 (the remainder is 0, so 1281 is a divisor of 1281)

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 1281 (i.e. 35.791060336347). 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 $\frac{N}{d} = D$ )

1281 / 1 = 1281 (the remainder is 0, so 1 and 1281 are divisors of 1281)
1281 / 2 = 640.5 (the remainder is 1, so 2 is not a divisor of 1281)
1281 / 3 = 427 (the remainder is 0, so 3 and 427 are divisors of 1281)
...
1281 / 34 = 37.676470588235 (the remainder is 23, so 34 is not a divisor of 1281)
1281 / 35 = 36.6 (the remainder is 21, so 35 is not a divisor of 1281)