What are the divisors of 7033?

1, 13, 541, 7033

There is a total of 4 positive divisors.
The sum of these divisors is 7588.
The arithmetic mean is 1897.

4 odd divisors

1, 13, 541, 7033

How to compute the divisors of 7033?

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 7033 by each of the numbers from 1 to 7033 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)

7033 / 1 = 7033 (the remainder is 0, so 1 is a divisor of 7033)
7033 / 2 = 3516.5 (the remainder is 1, so 2 is not a divisor of 7033)
7033 / 3 = 2344.3333333333 (the remainder is 1, so 3 is not a divisor of 7033)
...
7033 / 7032 = 1.0001422070535 (the remainder is 1, so 7032 is not a divisor of 7033)
7033 / 7033 = 1 (the remainder is 0, so 7033 is a divisor of 7033)

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 7033 (i.e. 83.86298349093). 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 $\frac{N}{d} = D$ )

7033 / 1 = 7033 (the remainder is 0, so 1 and 7033 are divisors of 7033)
7033 / 2 = 3516.5 (the remainder is 1, so 2 is not a divisor of 7033)
7033 / 3 = 2344.3333333333 (the remainder is 1, so 3 is not a divisor of 7033)
...
7033 / 82 = 85.768292682927 (the remainder is 63, so 82 is not a divisor of 7033)
7033 / 83 = 84.734939759036 (the remainder is 61, so 83 is not a divisor of 7033)