What are the divisors of 5145?

1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 343, 735, 1029, 1715, 5145

There is a total of 16 positive divisors.
The sum of these divisors is 9600.
The arithmetic mean is 600.

16 odd divisors

1, 3, 5, 7, 15, 21, 35, 49, 105, 147, 245, 343, 735, 1029, 1715, 5145

How to compute the divisors of 5145?

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 5145 by each of the numbers from 1 to 5145 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)

5145 / 1 = 5145 (the remainder is 0, so 1 is a divisor of 5145)
5145 / 2 = 2572.5 (the remainder is 1, so 2 is not a divisor of 5145)
5145 / 3 = 1715 (the remainder is 0, so 3 is a divisor of 5145)
...
5145 / 5144 = 1.0001944012442 (the remainder is 1, so 5144 is not a divisor of 5145)
5145 / 5145 = 1 (the remainder is 0, so 5145 is a divisor of 5145)

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 5145 (i.e. 71.728655361717). 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 $\frac{N}{d} = D$ )

5145 / 1 = 5145 (the remainder is 0, so 1 and 5145 are divisors of 5145)
5145 / 2 = 2572.5 (the remainder is 1, so 2 is not a divisor of 5145)
5145 / 3 = 1715 (the remainder is 0, so 3 and 1715 are divisors of 5145)
...
5145 / 70 = 73.5 (the remainder is 35, so 70 is not a divisor of 5145)
5145 / 71 = 72.464788732394 (the remainder is 33, so 71 is not a divisor of 5145)