What are the divisors of 2807?

1, 7, 401, 2807

There is a total of 4 positive divisors.
The sum of these divisors is 3216.
The arithmetic mean is 804.

4 odd divisors

1, 7, 401, 2807

How to compute the divisors of 2807?

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 2807 by each of the numbers from 1 to 2807 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)

2807 / 1 = 2807 (the remainder is 0, so 1 is a divisor of 2807)
2807 / 2 = 1403.5 (the remainder is 1, so 2 is not a divisor of 2807)
2807 / 3 = 935.66666666667 (the remainder is 2, so 3 is not a divisor of 2807)
...
2807 / 2806 = 1.0003563791875 (the remainder is 1, so 2806 is not a divisor of 2807)
2807 / 2807 = 1 (the remainder is 0, so 2807 is a divisor of 2807)

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 2807 (i.e. 52.981128715798). 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 $\frac{N}{d} = D$ )

2807 / 1 = 2807 (the remainder is 0, so 1 and 2807 are divisors of 2807)
2807 / 2 = 1403.5 (the remainder is 1, so 2 is not a divisor of 2807)
2807 / 3 = 935.66666666667 (the remainder is 2, so 3 is not a divisor of 2807)
...
2807 / 51 = 55.039215686275 (the remainder is 2, so 51 is not a divisor of 2807)
2807 / 52 = 53.980769230769 (the remainder is 51, so 52 is not a divisor of 2807)