What are the divisors of 7072?

1, 2, 4, 8, 13, 16, 17, 26, 32, 34, 52, 68, 104, 136, 208, 221, 272, 416, 442, 544, 884, 1768, 3536, 7072

There is a total of 24 positive divisors.
The sum of these divisors is 15876.
The arithmetic mean is 661.5.

20 even divisors

2, 4, 8, 16, 26, 32, 34, 52, 68, 104, 136, 208, 272, 416, 442, 544, 884, 1768, 3536, 7072

4 odd divisors

1, 13, 17, 221

How to compute the divisors of 7072?

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 7072 by each of the numbers from 1 to 7072 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)

7072 / 1 = 7072 (the remainder is 0, so 1 is a divisor of 7072)
7072 / 2 = 3536 (the remainder is 0, so 2 is a divisor of 7072)
7072 / 3 = 2357.3333333333 (the remainder is 1, so 3 is not a divisor of 7072)
...
7072 / 7071 = 1.0001414227125 (the remainder is 1, so 7071 is not a divisor of 7072)
7072 / 7072 = 1 (the remainder is 0, so 7072 is a divisor of 7072)

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 7072 (i.e. 84.095184166515). 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 $\frac{N}{d} = D$ )

7072 / 1 = 7072 (the remainder is 0, so 1 and 7072 are divisors of 7072)
7072 / 2 = 3536 (the remainder is 0, so 2 and 3536 are divisors of 7072)
7072 / 3 = 2357.3333333333 (the remainder is 1, so 3 is not a divisor of 7072)
...
7072 / 83 = 85.204819277108 (the remainder is 17, so 83 is not a divisor of 7072)
7072 / 84 = 84.190476190476 (the remainder is 16, so 84 is not a divisor of 7072)