What are the divisors of 5478?

1, 2, 3, 6, 11, 22, 33, 66, 83, 166, 249, 498, 913, 1826, 2739, 5478

There is a total of 16 positive divisors.
The sum of these divisors is 12096.
The arithmetic mean is 756.

8 even divisors

2, 6, 22, 66, 166, 498, 1826, 5478

8 odd divisors

1, 3, 11, 33, 83, 249, 913, 2739

How to compute the divisors of 5478?

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 5478 by each of the numbers from 1 to 5478 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)

5478 / 1 = 5478 (the remainder is 0, so 1 is a divisor of 5478)
5478 / 2 = 2739 (the remainder is 0, so 2 is a divisor of 5478)
5478 / 3 = 1826 (the remainder is 0, so 3 is a divisor of 5478)
...
5478 / 5477 = 1.0001825817053 (the remainder is 1, so 5477 is not a divisor of 5478)
5478 / 5478 = 1 (the remainder is 0, so 5478 is a divisor of 5478)

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 5478 (i.e. 74.013512279853). 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 $\frac{N}{d} = D$ )

5478 / 1 = 5478 (the remainder is 0, so 1 and 5478 are divisors of 5478)
5478 / 2 = 2739 (the remainder is 0, so 2 and 2739 are divisors of 5478)
5478 / 3 = 1826 (the remainder is 0, so 3 and 1826 are divisors of 5478)
...
5478 / 73 = 75.041095890411 (the remainder is 3, so 73 is not a divisor of 5478)
5478 / 74 = 74.027027027027 (the remainder is 2, so 74 is not a divisor of 5478)