What are the divisors of 7052?

1, 2, 4, 41, 43, 82, 86, 164, 172, 1763, 3526, 7052

There is a total of 12 positive divisors.
The sum of these divisors is 12936.
The arithmetic mean is 1078.

8 even divisors

2, 4, 82, 86, 164, 172, 3526, 7052

4 odd divisors

1, 41, 43, 1763

How to compute the divisors of 7052?

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 7052 by each of the numbers from 1 to 7052 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)

7052 / 1 = 7052 (the remainder is 0, so 1 is a divisor of 7052)
7052 / 2 = 3526 (the remainder is 0, so 2 is a divisor of 7052)
7052 / 3 = 2350.6666666667 (the remainder is 2, so 3 is not a divisor of 7052)
...
7052 / 7051 = 1.0001418238548 (the remainder is 1, so 7051 is not a divisor of 7052)
7052 / 7052 = 1 (the remainder is 0, so 7052 is a divisor of 7052)

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 7052 (i.e. 83.976187100868). 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 $\frac{N}{d} = D$ )

7052 / 1 = 7052 (the remainder is 0, so 1 and 7052 are divisors of 7052)
7052 / 2 = 3526 (the remainder is 0, so 2 and 3526 are divisors of 7052)
7052 / 3 = 2350.6666666667 (the remainder is 2, so 3 is not a divisor of 7052)
...
7052 / 82 = 86 (the remainder is 0, so 82 and 86 are divisors of 7052)
7052 / 83 = 84.963855421687 (the remainder is 80, so 83 is not a divisor of 7052)