What are the divisors of 5488?

1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 343, 392, 686, 784, 1372, 2744, 5488

There is a total of 20 positive divisors.
The sum of these divisors is 12400.
The arithmetic mean is 620.

16 even divisors

2, 4, 8, 14, 16, 28, 56, 98, 112, 196, 392, 686, 784, 1372, 2744, 5488

4 odd divisors

1, 7, 49, 343

How to compute the divisors of 5488?

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 5488 by each of the numbers from 1 to 5488 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)

5488 / 1 = 5488 (the remainder is 0, so 1 is a divisor of 5488)
5488 / 2 = 2744 (the remainder is 0, so 2 is a divisor of 5488)
5488 / 3 = 1829.3333333333 (the remainder is 1, so 3 is not a divisor of 5488)
...
5488 / 5487 = 1.0001822489521 (the remainder is 1, so 5487 is not a divisor of 5488)
5488 / 5488 = 1 (the remainder is 0, so 5488 is a divisor of 5488)

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 5488 (i.e. 74.081036709809). 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 $\frac{N}{d} = D$ )

5488 / 1 = 5488 (the remainder is 0, so 1 and 5488 are divisors of 5488)
5488 / 2 = 2744 (the remainder is 0, so 2 and 2744 are divisors of 5488)
5488 / 3 = 1829.3333333333 (the remainder is 1, so 3 is not a divisor of 5488)
...
5488 / 73 = 75.178082191781 (the remainder is 13, so 73 is not a divisor of 5488)
5488 / 74 = 74.162162162162 (the remainder is 12, so 74 is not a divisor of 5488)