What are the divisors of 8274?

1, 2, 3, 6, 7, 14, 21, 42, 197, 394, 591, 1182, 1379, 2758, 4137, 8274

There is a total of 16 positive divisors.
The sum of these divisors is 19008.
The arithmetic mean is 1188.

8 even divisors

2, 6, 14, 42, 394, 1182, 2758, 8274

8 odd divisors

1, 3, 7, 21, 197, 591, 1379, 4137

How to compute the divisors of 8274?

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 8274 by each of the numbers from 1 to 8274 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)

8274 / 1 = 8274 (the remainder is 0, so 1 is a divisor of 8274)
8274 / 2 = 4137 (the remainder is 0, so 2 is a divisor of 8274)
8274 / 3 = 2758 (the remainder is 0, so 3 is a divisor of 8274)
...
8274 / 8273 = 1.000120875136 (the remainder is 1, so 8273 is not a divisor of 8274)
8274 / 8274 = 1 (the remainder is 0, so 8274 is a divisor of 8274)

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 8274 (i.e. 90.961530330135). 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 $\frac{N}{d} = D$ )

8274 / 1 = 8274 (the remainder is 0, so 1 and 8274 are divisors of 8274)
8274 / 2 = 4137 (the remainder is 0, so 2 and 4137 are divisors of 8274)
8274 / 3 = 2758 (the remainder is 0, so 3 and 2758 are divisors of 8274)
...
8274 / 89 = 92.966292134831 (the remainder is 86, so 89 is not a divisor of 8274)
8274 / 90 = 91.933333333333 (the remainder is 84, so 90 is not a divisor of 8274)