What are the divisors of 7045?

1, 5, 1409, 7045

There is a total of 4 positive divisors.
The sum of these divisors is 8460.
The arithmetic mean is 2115.

4 odd divisors

1, 5, 1409, 7045

How to compute the divisors of 7045?

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 7045 by each of the numbers from 1 to 7045 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)

7045 / 1 = 7045 (the remainder is 0, so 1 is a divisor of 7045)
7045 / 2 = 3522.5 (the remainder is 1, so 2 is not a divisor of 7045)
7045 / 3 = 2348.3333333333 (the remainder is 1, so 3 is not a divisor of 7045)
...
7045 / 7044 = 1.0001419647927 (the remainder is 1, so 7044 is not a divisor of 7045)
7045 / 7045 = 1 (the remainder is 0, so 7045 is a divisor of 7045)

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 7045 (i.e. 83.934498270973). 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 $\frac{N}{d} = D$ )

7045 / 1 = 7045 (the remainder is 0, so 1 and 7045 are divisors of 7045)
7045 / 2 = 3522.5 (the remainder is 1, so 2 is not a divisor of 7045)
7045 / 3 = 2348.3333333333 (the remainder is 1, so 3 is not a divisor of 7045)
...
7045 / 82 = 85.914634146341 (the remainder is 75, so 82 is not a divisor of 7045)
7045 / 83 = 84.879518072289 (the remainder is 73, so 83 is not a divisor of 7045)