What are the divisors of 5480?

1, 2, 4, 5, 8, 10, 20, 40, 137, 274, 548, 685, 1096, 1370, 2740, 5480

There is a total of 16 positive divisors.
The sum of these divisors is 12420.
The arithmetic mean is 776.25.

12 even divisors

2, 4, 8, 10, 20, 40, 274, 548, 1096, 1370, 2740, 5480

4 odd divisors

1, 5, 137, 685

How to compute the divisors of 5480?

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 5480 by each of the numbers from 1 to 5480 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)

5480 / 1 = 5480 (the remainder is 0, so 1 is a divisor of 5480)
5480 / 2 = 2740 (the remainder is 0, so 2 is a divisor of 5480)
5480 / 3 = 1826.6666666667 (the remainder is 2, so 3 is not a divisor of 5480)
...
5480 / 5479 = 1.0001825150575 (the remainder is 1, so 5479 is not a divisor of 5480)
5480 / 5480 = 1 (the remainder is 0, so 5480 is a divisor of 5480)

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 5480 (i.e. 74.027022093287). 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 $\frac{N}{d} = D$ )

5480 / 1 = 5480 (the remainder is 0, so 1 and 5480 are divisors of 5480)
5480 / 2 = 2740 (the remainder is 0, so 2 and 2740 are divisors of 5480)
5480 / 3 = 1826.6666666667 (the remainder is 2, so 3 is not a divisor of 5480)
...
5480 / 73 = 75.068493150685 (the remainder is 5, so 73 is not a divisor of 5480)
5480 / 74 = 74.054054054054 (the remainder is 4, so 74 is not a divisor of 5480)