What are the divisors of 5072?

1, 2, 4, 8, 16, 317, 634, 1268, 2536, 5072

There is a total of 10 positive divisors.
The sum of these divisors is 9858.
The arithmetic mean is 985.8.

8 even divisors

2, 4, 8, 16, 634, 1268, 2536, 5072

2 odd divisors

1, 317

How to compute the divisors of 5072?

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 5072 by each of the numbers from 1 to 5072 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)

5072 / 1 = 5072 (the remainder is 0, so 1 is a divisor of 5072)
5072 / 2 = 2536 (the remainder is 0, so 2 is a divisor of 5072)
5072 / 3 = 1690.6666666667 (the remainder is 2, so 3 is not a divisor of 5072)
...
5072 / 5071 = 1.0001971997634 (the remainder is 1, so 5071 is not a divisor of 5072)
5072 / 5072 = 1 (the remainder is 0, so 5072 is a divisor of 5072)

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 5072 (i.e. 71.217975259059). 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 $\frac{N}{d} = D$ )

5072 / 1 = 5072 (the remainder is 0, so 1 and 5072 are divisors of 5072)
5072 / 2 = 2536 (the remainder is 0, so 2 and 2536 are divisors of 5072)
5072 / 3 = 1690.6666666667 (the remainder is 2, so 3 is not a divisor of 5072)
...
5072 / 70 = 72.457142857143 (the remainder is 32, so 70 is not a divisor of 5072)
5072 / 71 = 71.43661971831 (the remainder is 31, so 71 is not a divisor of 5072)