What are the divisors of 8157?

1, 3, 2719, 8157

There is a total of 4 positive divisors.
The sum of these divisors is 10880.
The arithmetic mean is 2720.

4 odd divisors

1, 3, 2719, 8157

How to compute the divisors of 8157?

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 8157 by each of the numbers from 1 to 8157 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)

8157 / 1 = 8157 (the remainder is 0, so 1 is a divisor of 8157)
8157 / 2 = 4078.5 (the remainder is 1, so 2 is not a divisor of 8157)
8157 / 3 = 2719 (the remainder is 0, so 3 is a divisor of 8157)
...
8157 / 8156 = 1.0001226091221 (the remainder is 1, so 8156 is not a divisor of 8157)
8157 / 8157 = 1 (the remainder is 0, so 8157 is a divisor of 8157)

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 8157 (i.e. 90.316111519485). 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 $\frac{N}{d} = D$ )

8157 / 1 = 8157 (the remainder is 0, so 1 and 8157 are divisors of 8157)
8157 / 2 = 4078.5 (the remainder is 1, so 2 is not a divisor of 8157)
8157 / 3 = 2719 (the remainder is 0, so 3 and 2719 are divisors of 8157)
...
8157 / 89 = 91.651685393258 (the remainder is 58, so 89 is not a divisor of 8157)
8157 / 90 = 90.633333333333 (the remainder is 57, so 90 is not a divisor of 8157)