What are the divisors of 1341?

1, 3, 9, 149, 447, 1341

There is a total of 6 positive divisors.
The sum of these divisors is 1950.
The arithmetic mean is 325.

6 odd divisors

1, 3, 9, 149, 447, 1341

How to compute the divisors of 1341?

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 1341 by each of the numbers from 1 to 1341 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)

1341 / 1 = 1341 (the remainder is 0, so 1 is a divisor of 1341)
1341 / 2 = 670.5 (the remainder is 1, so 2 is not a divisor of 1341)
1341 / 3 = 447 (the remainder is 0, so 3 is a divisor of 1341)
...
1341 / 1340 = 1.0007462686567 (the remainder is 1, so 1340 is not a divisor of 1341)
1341 / 1341 = 1 (the remainder is 0, so 1341 is a divisor of 1341)

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 1341 (i.e. 36.619666847201). 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 $\frac{N}{d} = D$ )

1341 / 1 = 1341 (the remainder is 0, so 1 and 1341 are divisors of 1341)
1341 / 2 = 670.5 (the remainder is 1, so 2 is not a divisor of 1341)
1341 / 3 = 447 (the remainder is 0, so 3 and 447 are divisors of 1341)
...
1341 / 35 = 38.314285714286 (the remainder is 11, so 35 is not a divisor of 1341)
1341 / 36 = 37.25 (the remainder is 9, so 36 is not a divisor of 1341)