What are the divisors of 5049?

1, 3, 9, 11, 17, 27, 33, 51, 99, 153, 187, 297, 459, 561, 1683, 5049

There is a total of 16 positive divisors.
The sum of these divisors is 8640.
The arithmetic mean is 540.

16 odd divisors

1, 3, 9, 11, 17, 27, 33, 51, 99, 153, 187, 297, 459, 561, 1683, 5049

How to compute the divisors of 5049?

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 5049 by each of the numbers from 1 to 5049 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)

5049 / 1 = 5049 (the remainder is 0, so 1 is a divisor of 5049)
5049 / 2 = 2524.5 (the remainder is 1, so 2 is not a divisor of 5049)
5049 / 3 = 1683 (the remainder is 0, so 3 is a divisor of 5049)
...
5049 / 5048 = 1.0001980982567 (the remainder is 1, so 5048 is not a divisor of 5049)
5049 / 5049 = 1 (the remainder is 0, so 5049 is a divisor of 5049)

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 5049 (i.e. 71.056315693962). 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 $\frac{N}{d} = D$ )

5049 / 1 = 5049 (the remainder is 0, so 1 and 5049 are divisors of 5049)
5049 / 2 = 2524.5 (the remainder is 1, so 2 is not a divisor of 5049)
5049 / 3 = 1683 (the remainder is 0, so 3 and 1683 are divisors of 5049)
...
5049 / 70 = 72.128571428571 (the remainder is 9, so 70 is not a divisor of 5049)
5049 / 71 = 71.112676056338 (the remainder is 8, so 71 is not a divisor of 5049)