What are the divisors of 8053?

1, 8053

There is a total of 2 positive divisors.
The sum of these divisors is 8054.
The arithmetic mean is 4027.

2 odd divisors

1, 8053

How to compute the divisors of 8053?

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 8053 by each of the numbers from 1 to 8053 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)

8053 / 1 = 8053 (the remainder is 0, so 1 is a divisor of 8053)
8053 / 2 = 4026.5 (the remainder is 1, so 2 is not a divisor of 8053)
8053 / 3 = 2684.3333333333 (the remainder is 1, so 3 is not a divisor of 8053)
...
8053 / 8052 = 1.0001241927471 (the remainder is 1, so 8052 is not a divisor of 8053)
8053 / 8053 = 1 (the remainder is 0, so 8053 is a divisor of 8053)

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 8053 (i.e. 89.738509013689). 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 $\frac{N}{d} = D$ )

8053 / 1 = 8053 (the remainder is 0, so 1 and 8053 are divisors of 8053)
8053 / 2 = 4026.5 (the remainder is 1, so 2 is not a divisor of 8053)
8053 / 3 = 2684.3333333333 (the remainder is 1, so 3 is not a divisor of 8053)
...
8053 / 88 = 91.511363636364 (the remainder is 45, so 88 is not a divisor of 8053)
8053 / 89 = 90.483146067416 (the remainder is 43, so 89 is not a divisor of 8053)