What are the divisors of 5147?

1, 5147

There is a total of 2 positive divisors.
The sum of these divisors is 5148.
The arithmetic mean is 2574.

2 odd divisors

1, 5147

How to compute the divisors of 5147?

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 5147 by each of the numbers from 1 to 5147 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)

5147 / 1 = 5147 (the remainder is 0, so 1 is a divisor of 5147)
5147 / 2 = 2573.5 (the remainder is 1, so 2 is not a divisor of 5147)
5147 / 3 = 1715.6666666667 (the remainder is 2, so 3 is not a divisor of 5147)
...
5147 / 5146 = 1.0001943256899 (the remainder is 1, so 5146 is not a divisor of 5147)
5147 / 5147 = 1 (the remainder is 0, so 5147 is a divisor of 5147)

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 5147 (i.e. 71.742595436742). 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 $\frac{N}{d} = D$ )

5147 / 1 = 5147 (the remainder is 0, so 1 and 5147 are divisors of 5147)
5147 / 2 = 2573.5 (the remainder is 1, so 2 is not a divisor of 5147)
5147 / 3 = 1715.6666666667 (the remainder is 2, so 3 is not a divisor of 5147)
...
5147 / 70 = 73.528571428571 (the remainder is 37, so 70 is not a divisor of 5147)
5147 / 71 = 72.492957746479 (the remainder is 35, so 71 is not a divisor of 5147)