What are the divisors of 8260?

1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 59, 70, 118, 140, 236, 295, 413, 590, 826, 1180, 1652, 2065, 4130, 8260

There is a total of 24 positive divisors.
The sum of these divisors is 20160.
The arithmetic mean is 840.

16 even divisors

2, 4, 10, 14, 20, 28, 70, 118, 140, 236, 590, 826, 1180, 1652, 4130, 8260

8 odd divisors

1, 5, 7, 35, 59, 295, 413, 2065

How to compute the divisors of 8260?

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 8260 by each of the numbers from 1 to 8260 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)

8260 / 1 = 8260 (the remainder is 0, so 1 is a divisor of 8260)
8260 / 2 = 4130 (the remainder is 0, so 2 is a divisor of 8260)
8260 / 3 = 2753.3333333333 (the remainder is 1, so 3 is not a divisor of 8260)
...
8260 / 8259 = 1.0001210800339 (the remainder is 1, so 8259 is not a divisor of 8260)
8260 / 8260 = 1 (the remainder is 0, so 8260 is a divisor of 8260)

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 8260 (i.e. 90.884542140014). 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 $\frac{N}{d} = D$ )

8260 / 1 = 8260 (the remainder is 0, so 1 and 8260 are divisors of 8260)
8260 / 2 = 4130 (the remainder is 0, so 2 and 4130 are divisors of 8260)
8260 / 3 = 2753.3333333333 (the remainder is 1, so 3 is not a divisor of 8260)
...
8260 / 89 = 92.808988764045 (the remainder is 72, so 89 is not a divisor of 8260)
8260 / 90 = 91.777777777778 (the remainder is 70, so 90 is not a divisor of 8260)