What are the divisors of 6049?

1, 23, 263, 6049

There is a total of 4 positive divisors.
The sum of these divisors is 6336.
The arithmetic mean is 1584.

4 odd divisors

1, 23, 263, 6049

How to compute the divisors of 6049?

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 6049 by each of the numbers from 1 to 6049 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)

6049 / 1 = 6049 (the remainder is 0, so 1 is a divisor of 6049)
6049 / 2 = 3024.5 (the remainder is 1, so 2 is not a divisor of 6049)
6049 / 3 = 2016.3333333333 (the remainder is 1, so 3 is not a divisor of 6049)
...
6049 / 6048 = 1.0001653439153 (the remainder is 1, so 6048 is not a divisor of 6049)
6049 / 6049 = 1 (the remainder is 0, so 6049 is a divisor of 6049)

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 6049 (i.e. 77.775317421403). 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 $\frac{N}{d} = D$ )

6049 / 1 = 6049 (the remainder is 0, so 1 and 6049 are divisors of 6049)
6049 / 2 = 3024.5 (the remainder is 1, so 2 is not a divisor of 6049)
6049 / 3 = 2016.3333333333 (the remainder is 1, so 3 is not a divisor of 6049)
...
6049 / 76 = 79.592105263158 (the remainder is 45, so 76 is not a divisor of 6049)
6049 / 77 = 78.558441558442 (the remainder is 43, so 77 is not a divisor of 6049)