What are the divisors of 5479?

1, 5479

There is a total of 2 positive divisors.
The sum of these divisors is 5480.
The arithmetic mean is 2740.

2 odd divisors

1, 5479

How to compute the divisors of 5479?

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 5479 by each of the numbers from 1 to 5479 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)

5479 / 1 = 5479 (the remainder is 0, so 1 is a divisor of 5479)
5479 / 2 = 2739.5 (the remainder is 1, so 2 is not a divisor of 5479)
5479 / 3 = 1826.3333333333 (the remainder is 1, so 3 is not a divisor of 5479)
...
5479 / 5478 = 1.0001825483753 (the remainder is 1, so 5478 is not a divisor of 5479)
5479 / 5479 = 1 (the remainder is 0, so 5479 is a divisor of 5479)

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 5479 (i.e. 74.020267494788). 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 $\frac{N}{d} = D$ )

5479 / 1 = 5479 (the remainder is 0, so 1 and 5479 are divisors of 5479)
5479 / 2 = 2739.5 (the remainder is 1, so 2 is not a divisor of 5479)
5479 / 3 = 1826.3333333333 (the remainder is 1, so 3 is not a divisor of 5479)
...
5479 / 73 = 75.054794520548 (the remainder is 4, so 73 is not a divisor of 5479)
5479 / 74 = 74.040540540541 (the remainder is 3, so 74 is not a divisor of 5479)