What are the divisors of 7090?

1, 2, 5, 10, 709, 1418, 3545, 7090

There is a total of 8 positive divisors.
The sum of these divisors is 12780.
The arithmetic mean is 1597.5.

4 even divisors

2, 10, 1418, 7090

4 odd divisors

1, 5, 709, 3545

How to compute the divisors of 7090?

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 7090 by each of the numbers from 1 to 7090 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)

7090 / 1 = 7090 (the remainder is 0, so 1 is a divisor of 7090)
7090 / 2 = 3545 (the remainder is 0, so 2 is a divisor of 7090)
7090 / 3 = 2363.3333333333 (the remainder is 1, so 3 is not a divisor of 7090)
...
7090 / 7089 = 1.0001410636197 (the remainder is 1, so 7089 is not a divisor of 7090)
7090 / 7090 = 1 (the remainder is 0, so 7090 is a divisor of 7090)

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 7090 (i.e. 84.202137740084). 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 $\frac{N}{d} = D$ )

7090 / 1 = 7090 (the remainder is 0, so 1 and 7090 are divisors of 7090)
7090 / 2 = 3545 (the remainder is 0, so 2 and 3545 are divisors of 7090)
7090 / 3 = 2363.3333333333 (the remainder is 1, so 3 is not a divisor of 7090)
...
7090 / 83 = 85.421686746988 (the remainder is 35, so 83 is not a divisor of 7090)
7090 / 84 = 84.404761904762 (the remainder is 34, so 84 is not a divisor of 7090)