What are the divisors of 5376?

1, 2, 3, 4, 6, 7, 8, 12, 14, 16, 21, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 128, 168, 192, 224, 256, 336, 384, 448, 672, 768, 896, 1344, 1792, 2688, 5376

There is a total of 36 positive divisors.
The sum of these divisors is 16352.
The arithmetic mean is 454.22222222222.

32 even divisors

2, 4, 6, 8, 12, 14, 16, 24, 28, 32, 42, 48, 56, 64, 84, 96, 112, 128, 168, 192, 224, 256, 336, 384, 448, 672, 768, 896, 1344, 1792, 2688, 5376

4 odd divisors

1, 3, 7, 21

How to compute the divisors of 5376?

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 5376 by each of the numbers from 1 to 5376 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)

5376 / 1 = 5376 (the remainder is 0, so 1 is a divisor of 5376)
5376 / 2 = 2688 (the remainder is 0, so 2 is a divisor of 5376)
5376 / 3 = 1792 (the remainder is 0, so 3 is a divisor of 5376)
...
5376 / 5375 = 1.0001860465116 (the remainder is 1, so 5375 is not a divisor of 5376)
5376 / 5376 = 1 (the remainder is 0, so 5376 is a divisor of 5376)

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 5376 (i.e. 73.321211119293). 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 $\frac{N}{d} = D$ )

5376 / 1 = 5376 (the remainder is 0, so 1 and 5376 are divisors of 5376)
5376 / 2 = 2688 (the remainder is 0, so 2 and 2688 are divisors of 5376)
5376 / 3 = 1792 (the remainder is 0, so 3 and 1792 are divisors of 5376)
...
5376 / 72 = 74.666666666667 (the remainder is 48, so 72 is not a divisor of 5376)
5376 / 73 = 73.643835616438 (the remainder is 47, so 73 is not a divisor of 5376)