What are the divisors of 7049?

1, 7, 19, 53, 133, 371, 1007, 7049

There is a total of 8 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 1080.

8 odd divisors

1, 7, 19, 53, 133, 371, 1007, 7049

How to compute the divisors of 7049?

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 7049 by each of the numbers from 1 to 7049 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)

7049 / 1 = 7049 (the remainder is 0, so 1 is a divisor of 7049)
7049 / 2 = 3524.5 (the remainder is 1, so 2 is not a divisor of 7049)
7049 / 3 = 2349.6666666667 (the remainder is 2, so 3 is not a divisor of 7049)
...
7049 / 7048 = 1.0001418842225 (the remainder is 1, so 7048 is not a divisor of 7049)
7049 / 7049 = 1 (the remainder is 0, so 7049 is a divisor of 7049)

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 7049 (i.e. 83.958322994209). 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 $\frac{N}{d} = D$ )

7049 / 1 = 7049 (the remainder is 0, so 1 and 7049 are divisors of 7049)
7049 / 2 = 3524.5 (the remainder is 1, so 2 is not a divisor of 7049)
7049 / 3 = 2349.6666666667 (the remainder is 2, so 3 is not a divisor of 7049)
...
7049 / 82 = 85.963414634146 (the remainder is 79, so 82 is not a divisor of 7049)
7049 / 83 = 84.927710843373 (the remainder is 77, so 83 is not a divisor of 7049)