What are the divisors of 6149?

1, 11, 13, 43, 143, 473, 559, 6149

There is a total of 8 positive divisors.
The sum of these divisors is 7392.
The arithmetic mean is 924.

8 odd divisors

1, 11, 13, 43, 143, 473, 559, 6149

How to compute the divisors of 6149?

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 6149 by each of the numbers from 1 to 6149 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)

6149 / 1 = 6149 (the remainder is 0, so 1 is a divisor of 6149)
6149 / 2 = 3074.5 (the remainder is 1, so 2 is not a divisor of 6149)
6149 / 3 = 2049.6666666667 (the remainder is 2, so 3 is not a divisor of 6149)
...
6149 / 6148 = 1.0001626545218 (the remainder is 1, so 6148 is not a divisor of 6149)
6149 / 6149 = 1 (the remainder is 0, so 6149 is a divisor of 6149)

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 6149 (i.e. 78.415559680461). 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 $\frac{N}{d} = D$ )

6149 / 1 = 6149 (the remainder is 0, so 1 and 6149 are divisors of 6149)
6149 / 2 = 3074.5 (the remainder is 1, so 2 is not a divisor of 6149)
6149 / 3 = 2049.6666666667 (the remainder is 2, so 3 is not a divisor of 6149)
...
6149 / 77 = 79.857142857143 (the remainder is 66, so 77 is not a divisor of 6149)
6149 / 78 = 78.833333333333 (the remainder is 65, so 78 is not a divisor of 6149)