What are the divisors of 5149?

1, 19, 271, 5149

There is a total of 4 positive divisors.
The sum of these divisors is 5440.
The arithmetic mean is 1360.

4 odd divisors

1, 19, 271, 5149

How to compute the divisors of 5149?

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 5149 by each of the numbers from 1 to 5149 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)

5149 / 1 = 5149 (the remainder is 0, so 1 is a divisor of 5149)
5149 / 2 = 2574.5 (the remainder is 1, so 2 is not a divisor of 5149)
5149 / 3 = 1716.3333333333 (the remainder is 1, so 3 is not a divisor of 5149)
...
5149 / 5148 = 1.0001942501943 (the remainder is 1, so 5148 is not a divisor of 5149)
5149 / 5149 = 1 (the remainder is 0, so 5149 is a divisor of 5149)

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 5149 (i.e. 71.756532803641). 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 $\frac{N}{d} = D$ )

5149 / 1 = 5149 (the remainder is 0, so 1 and 5149 are divisors of 5149)
5149 / 2 = 2574.5 (the remainder is 1, so 2 is not a divisor of 5149)
5149 / 3 = 1716.3333333333 (the remainder is 1, so 3 is not a divisor of 5149)
...
5149 / 70 = 73.557142857143 (the remainder is 39, so 70 is not a divisor of 5149)
5149 / 71 = 72.521126760563 (the remainder is 37, so 71 is not a divisor of 5149)