What are the divisors of 7010?

1, 2, 5, 10, 701, 1402, 3505, 7010

There is a total of 8 positive divisors.
The sum of these divisors is 12636.
The arithmetic mean is 1579.5.

4 even divisors

2, 10, 1402, 7010

4 odd divisors

1, 5, 701, 3505

How to compute the divisors of 7010?

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 7010 by each of the numbers from 1 to 7010 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)

7010 / 1 = 7010 (the remainder is 0, so 1 is a divisor of 7010)
7010 / 2 = 3505 (the remainder is 0, so 2 is a divisor of 7010)
7010 / 3 = 2336.6666666667 (the remainder is 2, so 3 is not a divisor of 7010)
...
7010 / 7009 = 1.0001426737052 (the remainder is 1, so 7009 is not a divisor of 7010)
7010 / 7010 = 1 (the remainder is 0, so 7010 is a divisor of 7010)

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 7010 (i.e. 83.725742755738). 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 $\frac{N}{d} = D$ )

7010 / 1 = 7010 (the remainder is 0, so 1 and 7010 are divisors of 7010)
7010 / 2 = 3505 (the remainder is 0, so 2 and 3505 are divisors of 7010)
7010 / 3 = 2336.6666666667 (the remainder is 2, so 3 is not a divisor of 7010)
...
7010 / 82 = 85.487804878049 (the remainder is 40, so 82 is not a divisor of 7010)
7010 / 83 = 84.457831325301 (the remainder is 38, so 83 is not a divisor of 7010)