What are the divisors of 6053?

1, 6053

There is a total of 2 positive divisors.
The sum of these divisors is 6054.
The arithmetic mean is 3027.

2 odd divisors

1, 6053

How to compute the divisors of 6053?

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 6053 by each of the numbers from 1 to 6053 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)

6053 / 1 = 6053 (the remainder is 0, so 1 is a divisor of 6053)
6053 / 2 = 3026.5 (the remainder is 1, so 2 is not a divisor of 6053)
6053 / 3 = 2017.6666666667 (the remainder is 2, so 3 is not a divisor of 6053)
...
6053 / 6052 = 1.0001652346332 (the remainder is 1, so 6052 is not a divisor of 6053)
6053 / 6053 = 1 (the remainder is 0, so 6053 is a divisor of 6053)

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 6053 (i.e. 77.80102827084). 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 $\frac{N}{d} = D$ )

6053 / 1 = 6053 (the remainder is 0, so 1 and 6053 are divisors of 6053)
6053 / 2 = 3026.5 (the remainder is 1, so 2 is not a divisor of 6053)
6053 / 3 = 2017.6666666667 (the remainder is 2, so 3 is not a divisor of 6053)
...
6053 / 76 = 79.644736842105 (the remainder is 49, so 76 is not a divisor of 6053)
6053 / 77 = 78.61038961039 (the remainder is 47, so 77 is not a divisor of 6053)