What are the divisors of 7051?

1, 11, 641, 7051

There is a total of 4 positive divisors.
The sum of these divisors is 7704.
The arithmetic mean is 1926.

4 odd divisors

1, 11, 641, 7051

How to compute the divisors of 7051?

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 7051 by each of the numbers from 1 to 7051 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)

7051 / 1 = 7051 (the remainder is 0, so 1 is a divisor of 7051)
7051 / 2 = 3525.5 (the remainder is 1, so 2 is not a divisor of 7051)
7051 / 3 = 2350.3333333333 (the remainder is 1, so 3 is not a divisor of 7051)
...
7051 / 7050 = 1.0001418439716 (the remainder is 1, so 7050 is not a divisor of 7051)
7051 / 7051 = 1 (the remainder is 0, so 7051 is a divisor of 7051)

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 7051 (i.e. 83.970232820923). 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 $\frac{N}{d} = D$ )

7051 / 1 = 7051 (the remainder is 0, so 1 and 7051 are divisors of 7051)
7051 / 2 = 3525.5 (the remainder is 1, so 2 is not a divisor of 7051)
7051 / 3 = 2350.3333333333 (the remainder is 1, so 3 is not a divisor of 7051)
...
7051 / 82 = 85.987804878049 (the remainder is 81, so 82 is not a divisor of 7051)
7051 / 83 = 84.951807228916 (the remainder is 79, so 83 is not a divisor of 7051)