What are the divisors of 5378?

1, 2, 2689, 5378

There is a total of 4 positive divisors.
The sum of these divisors is 8070.
The arithmetic mean is 2017.5.

2 even divisors

2, 5378

2 odd divisors

1, 2689

How to compute the divisors of 5378?

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 5378 by each of the numbers from 1 to 5378 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)

5378 / 1 = 5378 (the remainder is 0, so 1 is a divisor of 5378)
5378 / 2 = 2689 (the remainder is 0, so 2 is a divisor of 5378)
5378 / 3 = 1792.6666666667 (the remainder is 2, so 3 is not a divisor of 5378)
...
5378 / 5377 = 1.0001859773108 (the remainder is 1, so 5377 is not a divisor of 5378)
5378 / 5378 = 1 (the remainder is 0, so 5378 is a divisor of 5378)

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 5378 (i.e. 73.334848469196). 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 $\frac{N}{d} = D$ )

5378 / 1 = 5378 (the remainder is 0, so 1 and 5378 are divisors of 5378)
5378 / 2 = 2689 (the remainder is 0, so 2 and 2689 are divisors of 5378)
5378 / 3 = 1792.6666666667 (the remainder is 2, so 3 is not a divisor of 5378)
...
5378 / 72 = 74.694444444444 (the remainder is 50, so 72 is not a divisor of 5378)
5378 / 73 = 73.671232876712 (the remainder is 49, so 73 is not a divisor of 5378)