What are the divisors of 7070?

1, 2, 5, 7, 10, 14, 35, 70, 101, 202, 505, 707, 1010, 1414, 3535, 7070

There is a total of 16 positive divisors.
The sum of these divisors is 14688.
The arithmetic mean is 918.

8 even divisors

2, 10, 14, 70, 202, 1010, 1414, 7070

8 odd divisors

1, 5, 7, 35, 101, 505, 707, 3535

How to compute the divisors of 7070?

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 7070 by each of the numbers from 1 to 7070 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)

7070 / 1 = 7070 (the remainder is 0, so 1 is a divisor of 7070)
7070 / 2 = 3535 (the remainder is 0, so 2 is a divisor of 7070)
7070 / 3 = 2356.6666666667 (the remainder is 2, so 3 is not a divisor of 7070)
...
7070 / 7069 = 1.0001414627246 (the remainder is 1, so 7069 is not a divisor of 7070)
7070 / 7070 = 1 (the remainder is 0, so 7070 is a divisor of 7070)

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 7070 (i.e. 84.083292038312). 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 $\frac{N}{d} = D$ )

7070 / 1 = 7070 (the remainder is 0, so 1 and 7070 are divisors of 7070)
7070 / 2 = 3535 (the remainder is 0, so 2 and 3535 are divisors of 7070)
7070 / 3 = 2356.6666666667 (the remainder is 2, so 3 is not a divisor of 7070)
...
7070 / 83 = 85.180722891566 (the remainder is 15, so 83 is not a divisor of 7070)
7070 / 84 = 84.166666666667 (the remainder is 14, so 84 is not a divisor of 7070)