What are the divisors of 7013?

1, 7013

There is a total of 2 positive divisors.
The sum of these divisors is 7014.
The arithmetic mean is 3507.

2 odd divisors

1, 7013

How to compute the divisors of 7013?

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 7013 by each of the numbers from 1 to 7013 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)

7013 / 1 = 7013 (the remainder is 0, so 1 is a divisor of 7013)
7013 / 2 = 3506.5 (the remainder is 1, so 2 is not a divisor of 7013)
7013 / 3 = 2337.6666666667 (the remainder is 2, so 3 is not a divisor of 7013)
...
7013 / 7012 = 1.000142612664 (the remainder is 1, so 7012 is not a divisor of 7013)
7013 / 7013 = 1 (the remainder is 0, so 7013 is a divisor of 7013)

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 7013 (i.e. 83.743656476177). 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 $\frac{N}{d} = D$ )

7013 / 1 = 7013 (the remainder is 0, so 1 and 7013 are divisors of 7013)
7013 / 2 = 3506.5 (the remainder is 1, so 2 is not a divisor of 7013)
7013 / 3 = 2337.6666666667 (the remainder is 2, so 3 is not a divisor of 7013)
...
7013 / 82 = 85.524390243902 (the remainder is 43, so 82 is not a divisor of 7013)
7013 / 83 = 84.493975903614 (the remainder is 41, so 83 is not a divisor of 7013)