What are the divisors of 8254?

1, 2, 4127, 8254

There is a total of 4 positive divisors.
The sum of these divisors is 12384.
The arithmetic mean is 3096.

2 even divisors

2, 8254

2 odd divisors

1, 4127

How to compute the divisors of 8254?

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 8254 by each of the numbers from 1 to 8254 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)

8254 / 1 = 8254 (the remainder is 0, so 1 is a divisor of 8254)
8254 / 2 = 4127 (the remainder is 0, so 2 is a divisor of 8254)
8254 / 3 = 2751.3333333333 (the remainder is 1, so 3 is not a divisor of 8254)
...
8254 / 8253 = 1.0001211680601 (the remainder is 1, so 8253 is not a divisor of 8254)
8254 / 8254 = 1 (the remainder is 0, so 8254 is a divisor of 8254)

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 8254 (i.e. 90.851527229871). 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 $\frac{N}{d} = D$ )

8254 / 1 = 8254 (the remainder is 0, so 1 and 8254 are divisors of 8254)
8254 / 2 = 4127 (the remainder is 0, so 2 and 4127 are divisors of 8254)
8254 / 3 = 2751.3333333333 (the remainder is 1, so 3 is not a divisor of 8254)
...
8254 / 89 = 92.741573033708 (the remainder is 66, so 89 is not a divisor of 8254)
8254 / 90 = 91.711111111111 (the remainder is 64, so 90 is not a divisor of 8254)