What are the divisors of 7057?

1, 7057

There is a total of 2 positive divisors.
The sum of these divisors is 7058.
The arithmetic mean is 3529.

2 odd divisors

1, 7057

How to compute the divisors of 7057?

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 7057 by each of the numbers from 1 to 7057 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)

7057 / 1 = 7057 (the remainder is 0, so 1 is a divisor of 7057)
7057 / 2 = 3528.5 (the remainder is 1, so 2 is not a divisor of 7057)
7057 / 3 = 2352.3333333333 (the remainder is 1, so 3 is not a divisor of 7057)
...
7057 / 7056 = 1.000141723356 (the remainder is 1, so 7056 is not a divisor of 7057)
7057 / 7057 = 1 (the remainder is 0, so 7057 is a divisor of 7057)

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 7057 (i.e. 84.005952170069). 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 $\frac{N}{d} = D$ )

7057 / 1 = 7057 (the remainder is 0, so 1 and 7057 are divisors of 7057)
7057 / 2 = 3528.5 (the remainder is 1, so 2 is not a divisor of 7057)
7057 / 3 = 2352.3333333333 (the remainder is 1, so 3 is not a divisor of 7057)
...
7057 / 83 = 85.024096385542 (the remainder is 2, so 83 is not a divisor of 7057)
7057 / 84 = 84.011904761905 (the remainder is 1, so 84 is not a divisor of 7057)