What are the divisors of 7037?

1, 31, 227, 7037

There is a total of 4 positive divisors.
The sum of these divisors is 7296.
The arithmetic mean is 1824.

4 odd divisors

1, 31, 227, 7037

How to compute the divisors of 7037?

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 7037 by each of the numbers from 1 to 7037 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)

7037 / 1 = 7037 (the remainder is 0, so 1 is a divisor of 7037)
7037 / 2 = 3518.5 (the remainder is 1, so 2 is not a divisor of 7037)
7037 / 3 = 2345.6666666667 (the remainder is 2, so 3 is not a divisor of 7037)
...
7037 / 7036 = 1.0001421262081 (the remainder is 1, so 7036 is not a divisor of 7037)
7037 / 7037 = 1 (the remainder is 0, so 7037 is a divisor of 7037)

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 7037 (i.e. 83.886828525103). 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 $\frac{N}{d} = D$ )

7037 / 1 = 7037 (the remainder is 0, so 1 and 7037 are divisors of 7037)
7037 / 2 = 3518.5 (the remainder is 1, so 2 is not a divisor of 7037)
7037 / 3 = 2345.6666666667 (the remainder is 2, so 3 is not a divisor of 7037)
...
7037 / 82 = 85.817073170732 (the remainder is 67, so 82 is not a divisor of 7037)
7037 / 83 = 84.78313253012 (the remainder is 65, so 83 is not a divisor of 7037)