What are the divisors of 8151?

1, 3, 11, 13, 19, 33, 39, 57, 143, 209, 247, 429, 627, 741, 2717, 8151

There is a total of 16 positive divisors.
The sum of these divisors is 13440.
The arithmetic mean is 840.

16 odd divisors

1, 3, 11, 13, 19, 33, 39, 57, 143, 209, 247, 429, 627, 741, 2717, 8151

How to compute the divisors of 8151?

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 8151 by each of the numbers from 1 to 8151 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)

8151 / 1 = 8151 (the remainder is 0, so 1 is a divisor of 8151)
8151 / 2 = 4075.5 (the remainder is 1, so 2 is not a divisor of 8151)
8151 / 3 = 2717 (the remainder is 0, so 3 is a divisor of 8151)
...
8151 / 8150 = 1.0001226993865 (the remainder is 1, so 8150 is not a divisor of 8151)
8151 / 8151 = 1 (the remainder is 0, so 8151 is a divisor of 8151)

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 8151 (i.e. 90.282888744213). 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 $\frac{N}{d} = D$ )

8151 / 1 = 8151 (the remainder is 0, so 1 and 8151 are divisors of 8151)
8151 / 2 = 4075.5 (the remainder is 1, so 2 is not a divisor of 8151)
8151 / 3 = 2717 (the remainder is 0, so 3 and 2717 are divisors of 8151)
...
8151 / 89 = 91.584269662921 (the remainder is 52, so 89 is not a divisor of 8151)
8151 / 90 = 90.566666666667 (the remainder is 51, so 90 is not a divisor of 8151)