What are the divisors of 7099?

1, 31, 229, 7099

There is a total of 4 positive divisors.
The sum of these divisors is 7360.
The arithmetic mean is 1840.

4 odd divisors

1, 31, 229, 7099

How to compute the divisors of 7099?

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 7099 by each of the numbers from 1 to 7099 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)

7099 / 1 = 7099 (the remainder is 0, so 1 is a divisor of 7099)
7099 / 2 = 3549.5 (the remainder is 1, so 2 is not a divisor of 7099)
7099 / 3 = 2366.3333333333 (the remainder is 1, so 3 is not a divisor of 7099)
...
7099 / 7098 = 1.0001408847563 (the remainder is 1, so 7098 is not a divisor of 7099)
7099 / 7099 = 1 (the remainder is 0, so 7099 is a divisor of 7099)

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 7099 (i.e. 84.255563614517). 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 $\frac{N}{d} = D$ )

7099 / 1 = 7099 (the remainder is 0, so 1 and 7099 are divisors of 7099)
7099 / 2 = 3549.5 (the remainder is 1, so 2 is not a divisor of 7099)
7099 / 3 = 2366.3333333333 (the remainder is 1, so 3 is not a divisor of 7099)
...
7099 / 83 = 85.530120481928 (the remainder is 44, so 83 is not a divisor of 7099)
7099 / 84 = 84.511904761905 (the remainder is 43, so 84 is not a divisor of 7099)