What are the divisors of 7040?

1, 2, 4, 5, 8, 10, 11, 16, 20, 22, 32, 40, 44, 55, 64, 80, 88, 110, 128, 160, 176, 220, 320, 352, 440, 640, 704, 880, 1408, 1760, 3520, 7040

There is a total of 32 positive divisors.
The sum of these divisors is 18360.
The arithmetic mean is 573.75.

28 even divisors

2, 4, 8, 10, 16, 20, 22, 32, 40, 44, 64, 80, 88, 110, 128, 160, 176, 220, 320, 352, 440, 640, 704, 880, 1408, 1760, 3520, 7040

4 odd divisors

1, 5, 11, 55

How to compute the divisors of 7040?

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 7040 by each of the numbers from 1 to 7040 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)

7040 / 1 = 7040 (the remainder is 0, so 1 is a divisor of 7040)
7040 / 2 = 3520 (the remainder is 0, so 2 is a divisor of 7040)
7040 / 3 = 2346.6666666667 (the remainder is 2, so 3 is not a divisor of 7040)
...
7040 / 7039 = 1.0001420656343 (the remainder is 1, so 7039 is not a divisor of 7040)
7040 / 7040 = 1 (the remainder is 0, so 7040 is a divisor of 7040)

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 7040 (i.e. 83.904707853612). 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 $\frac{N}{d} = D$ )

7040 / 1 = 7040 (the remainder is 0, so 1 and 7040 are divisors of 7040)
7040 / 2 = 3520 (the remainder is 0, so 2 and 3520 are divisors of 7040)
7040 / 3 = 2346.6666666667 (the remainder is 2, so 3 is not a divisor of 7040)
...
7040 / 82 = 85.853658536585 (the remainder is 70, so 82 is not a divisor of 7040)
7040 / 83 = 84.819277108434 (the remainder is 68, so 83 is not a divisor of 7040)