What are the divisors of 1471?

1, 1471

There is a total of 2 positive divisors.
The sum of these divisors is 1472.
The arithmetic mean is 736.

2 odd divisors

1, 1471

How to compute the divisors of 1471?

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 1471 by each of the numbers from 1 to 1471 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)

1471 / 1 = 1471 (the remainder is 0, so 1 is a divisor of 1471)
1471 / 2 = 735.5 (the remainder is 1, so 2 is not a divisor of 1471)
1471 / 3 = 490.33333333333 (the remainder is 1, so 3 is not a divisor of 1471)
...
1471 / 1470 = 1.0006802721088 (the remainder is 1, so 1470 is not a divisor of 1471)
1471 / 1471 = 1 (the remainder is 0, so 1471 is a divisor of 1471)

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 1471 (i.e. 38.35361782153). 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 $\frac{N}{d} = D$ )

1471 / 1 = 1471 (the remainder is 0, so 1 and 1471 are divisors of 1471)
1471 / 2 = 735.5 (the remainder is 1, so 2 is not a divisor of 1471)
1471 / 3 = 490.33333333333 (the remainder is 1, so 3 is not a divisor of 1471)
...
1471 / 37 = 39.756756756757 (the remainder is 28, so 37 is not a divisor of 1471)
1471 / 38 = 38.710526315789 (the remainder is 27, so 38 is not a divisor of 1471)