What are the divisors of 8261?

1, 11, 751, 8261

There is a total of 4 positive divisors.
The sum of these divisors is 9024.
The arithmetic mean is 2256.

4 odd divisors

1, 11, 751, 8261

How to compute the divisors of 8261?

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 8261 by each of the numbers from 1 to 8261 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)

8261 / 1 = 8261 (the remainder is 0, so 1 is a divisor of 8261)
8261 / 2 = 4130.5 (the remainder is 1, so 2 is not a divisor of 8261)
8261 / 3 = 2753.6666666667 (the remainder is 2, so 3 is not a divisor of 8261)
...
8261 / 8260 = 1.0001210653753 (the remainder is 1, so 8260 is not a divisor of 8261)
8261 / 8261 = 1 (the remainder is 0, so 8261 is a divisor of 8261)

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 8261 (i.e. 90.890043459116). 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 $\frac{N}{d} = D$ )

8261 / 1 = 8261 (the remainder is 0, so 1 and 8261 are divisors of 8261)
8261 / 2 = 4130.5 (the remainder is 1, so 2 is not a divisor of 8261)
8261 / 3 = 2753.6666666667 (the remainder is 2, so 3 is not a divisor of 8261)
...
8261 / 89 = 92.820224719101 (the remainder is 73, so 89 is not a divisor of 8261)
8261 / 90 = 91.788888888889 (the remainder is 71, so 90 is not a divisor of 8261)