What are the divisors of 1447?

1, 1447

There is a total of 2 positive divisors.
The sum of these divisors is 1448.
The arithmetic mean is 724.

2 odd divisors

1, 1447

How to compute the divisors of 1447?

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 1447 by each of the numbers from 1 to 1447 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)

1447 / 1 = 1447 (the remainder is 0, so 1 is a divisor of 1447)
1447 / 2 = 723.5 (the remainder is 1, so 2 is not a divisor of 1447)
1447 / 3 = 482.33333333333 (the remainder is 1, so 3 is not a divisor of 1447)
...
1447 / 1446 = 1.0006915629322 (the remainder is 1, so 1446 is not a divisor of 1447)
1447 / 1447 = 1 (the remainder is 0, so 1447 is a divisor of 1447)

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 1447 (i.e. 38.03945320322). 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 $\frac{N}{d} = D$ )

1447 / 1 = 1447 (the remainder is 0, so 1 and 1447 are divisors of 1447)
1447 / 2 = 723.5 (the remainder is 1, so 2 is not a divisor of 1447)
1447 / 3 = 482.33333333333 (the remainder is 1, so 3 is not a divisor of 1447)
...
1447 / 37 = 39.108108108108 (the remainder is 4, so 37 is not a divisor of 1447)
1447 / 38 = 38.078947368421 (the remainder is 3, so 38 is not a divisor of 1447)