What are the divisors of 2471?

1, 7, 353, 2471

There is a total of 4 positive divisors.
The sum of these divisors is 2832.
The arithmetic mean is 708.

4 odd divisors

1, 7, 353, 2471

How to compute the divisors of 2471?

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 2471 by each of the numbers from 1 to 2471 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)

2471 / 1 = 2471 (the remainder is 0, so 1 is a divisor of 2471)
2471 / 2 = 1235.5 (the remainder is 1, so 2 is not a divisor of 2471)
2471 / 3 = 823.66666666667 (the remainder is 2, so 3 is not a divisor of 2471)
...
2471 / 2470 = 1.0004048582996 (the remainder is 1, so 2470 is not a divisor of 2471)
2471 / 2471 = 1 (the remainder is 0, so 2471 is a divisor of 2471)

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 2471 (i.e. 49.709154086546). 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 $\frac{N}{d} = D$ )

2471 / 1 = 2471 (the remainder is 0, so 1 and 2471 are divisors of 2471)
2471 / 2 = 1235.5 (the remainder is 1, so 2 is not a divisor of 2471)
2471 / 3 = 823.66666666667 (the remainder is 2, so 3 is not a divisor of 2471)
...
2471 / 48 = 51.479166666667 (the remainder is 23, so 48 is not a divisor of 2471)
2471 / 49 = 50.428571428571 (the remainder is 21, so 49 is not a divisor of 2471)