What are the divisors of 7024?

1, 2, 4, 8, 16, 439, 878, 1756, 3512, 7024

There is a total of 10 positive divisors.
The sum of these divisors is 13640.
The arithmetic mean is 1364.

8 even divisors

2, 4, 8, 16, 878, 1756, 3512, 7024

2 odd divisors

1, 439

How to compute the divisors of 7024?

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 7024 by each of the numbers from 1 to 7024 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)

7024 / 1 = 7024 (the remainder is 0, so 1 is a divisor of 7024)
7024 / 2 = 3512 (the remainder is 0, so 2 is a divisor of 7024)
7024 / 3 = 2341.3333333333 (the remainder is 1, so 3 is not a divisor of 7024)
...
7024 / 7023 = 1.0001423892923 (the remainder is 1, so 7023 is not a divisor of 7024)
7024 / 7024 = 1 (the remainder is 0, so 7024 is a divisor of 7024)

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 7024 (i.e. 83.809307359028). 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 $\frac{N}{d} = D$ )

7024 / 1 = 7024 (the remainder is 0, so 1 and 7024 are divisors of 7024)
7024 / 2 = 3512 (the remainder is 0, so 2 and 3512 are divisors of 7024)
7024 / 3 = 2341.3333333333 (the remainder is 1, so 3 is not a divisor of 7024)
...
7024 / 82 = 85.658536585366 (the remainder is 54, so 82 is not a divisor of 7024)
7024 / 83 = 84.626506024096 (the remainder is 52, so 83 is not a divisor of 7024)