What are the divisors of 8029?

1, 7, 31, 37, 217, 259, 1147, 8029

There is a total of 8 positive divisors.
The sum of these divisors is 9728.
The arithmetic mean is 1216.

8 odd divisors

1, 7, 31, 37, 217, 259, 1147, 8029

How to compute the divisors of 8029?

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 8029 by each of the numbers from 1 to 8029 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)

8029 / 1 = 8029 (the remainder is 0, so 1 is a divisor of 8029)
8029 / 2 = 4014.5 (the remainder is 1, so 2 is not a divisor of 8029)
8029 / 3 = 2676.3333333333 (the remainder is 1, so 3 is not a divisor of 8029)
...
8029 / 8028 = 1.0001245640259 (the remainder is 1, so 8028 is not a divisor of 8029)
8029 / 8029 = 1 (the remainder is 0, so 8029 is a divisor of 8029)

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 8029 (i.e. 89.604687377391). 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 $\frac{N}{d} = D$ )

8029 / 1 = 8029 (the remainder is 0, so 1 and 8029 are divisors of 8029)
8029 / 2 = 4014.5 (the remainder is 1, so 2 is not a divisor of 8029)
8029 / 3 = 2676.3333333333 (the remainder is 1, so 3 is not a divisor of 8029)
...
8029 / 88 = 91.238636363636 (the remainder is 21, so 88 is not a divisor of 8029)
8029 / 89 = 90.213483146067 (the remainder is 19, so 89 is not a divisor of 8029)