What are the divisors of 8149?

1, 29, 281, 8149

There is a total of 4 positive divisors.
The sum of these divisors is 8460.
The arithmetic mean is 2115.

4 odd divisors

1, 29, 281, 8149

How to compute the divisors of 8149?

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 8149 by each of the numbers from 1 to 8149 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)

8149 / 1 = 8149 (the remainder is 0, so 1 is a divisor of 8149)
8149 / 2 = 4074.5 (the remainder is 1, so 2 is not a divisor of 8149)
8149 / 3 = 2716.3333333333 (the remainder is 1, so 3 is not a divisor of 8149)
...
8149 / 8148 = 1.0001227295042 (the remainder is 1, so 8148 is not a divisor of 8149)
8149 / 8149 = 1 (the remainder is 0, so 8149 is a divisor of 8149)

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 8149 (i.e. 90.27181176868). 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 $\frac{N}{d} = D$ )

8149 / 1 = 8149 (the remainder is 0, so 1 and 8149 are divisors of 8149)
8149 / 2 = 4074.5 (the remainder is 1, so 2 is not a divisor of 8149)
8149 / 3 = 2716.3333333333 (the remainder is 1, so 3 is not a divisor of 8149)
...
8149 / 89 = 91.561797752809 (the remainder is 50, so 89 is not a divisor of 8149)
8149 / 90 = 90.544444444444 (the remainder is 49, so 90 is not a divisor of 8149)