What are the divisors of 7034?

1, 2, 3517, 7034

There is a total of 4 positive divisors.
The sum of these divisors is 10554.
The arithmetic mean is 2638.5.

2 even divisors

2, 7034

2 odd divisors

1, 3517

How to compute the divisors of 7034?

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 7034 by each of the numbers from 1 to 7034 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)

7034 / 1 = 7034 (the remainder is 0, so 1 is a divisor of 7034)
7034 / 2 = 3517 (the remainder is 0, so 2 is a divisor of 7034)
7034 / 3 = 2344.6666666667 (the remainder is 2, so 3 is not a divisor of 7034)
...
7034 / 7033 = 1.0001421868335 (the remainder is 1, so 7033 is not a divisor of 7034)
7034 / 7034 = 1 (the remainder is 0, so 7034 is a divisor of 7034)

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 7034 (i.e. 83.868945385047). 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 $\frac{N}{d} = D$ )

7034 / 1 = 7034 (the remainder is 0, so 1 and 7034 are divisors of 7034)
7034 / 2 = 3517 (the remainder is 0, so 2 and 3517 are divisors of 7034)
7034 / 3 = 2344.6666666667 (the remainder is 2, so 3 is not a divisor of 7034)
...
7034 / 82 = 85.780487804878 (the remainder is 64, so 82 is not a divisor of 7034)
7034 / 83 = 84.746987951807 (the remainder is 62, so 83 is not a divisor of 7034)