What are the divisors of 7048?

1, 2, 4, 8, 881, 1762, 3524, 7048

There is a total of 8 positive divisors.
The sum of these divisors is 13230.
The arithmetic mean is 1653.75.

6 even divisors

2, 4, 8, 1762, 3524, 7048

2 odd divisors

1, 881

How to compute the divisors of 7048?

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 7048 by each of the numbers from 1 to 7048 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)

7048 / 1 = 7048 (the remainder is 0, so 1 is a divisor of 7048)
7048 / 2 = 3524 (the remainder is 0, so 2 is a divisor of 7048)
7048 / 3 = 2349.3333333333 (the remainder is 1, so 3 is not a divisor of 7048)
...
7048 / 7047 = 1.0001419043565 (the remainder is 1, so 7047 is not a divisor of 7048)
7048 / 7048 = 1 (the remainder is 0, so 7048 is a divisor of 7048)

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 7048 (i.e. 83.952367447261). 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 $\frac{N}{d} = D$ )

7048 / 1 = 7048 (the remainder is 0, so 1 and 7048 are divisors of 7048)
7048 / 2 = 3524 (the remainder is 0, so 2 and 3524 are divisors of 7048)
7048 / 3 = 2349.3333333333 (the remainder is 1, so 3 is not a divisor of 7048)
...
7048 / 82 = 85.951219512195 (the remainder is 78, so 82 is not a divisor of 7048)
7048 / 83 = 84.915662650602 (the remainder is 76, so 83 is not a divisor of 7048)