What are the divisors of 5250?

1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 25, 30, 35, 42, 50, 70, 75, 105, 125, 150, 175, 210, 250, 350, 375, 525, 750, 875, 1050, 1750, 2625, 5250

There is a total of 32 positive divisors.
The sum of these divisors is 14976.
The arithmetic mean is 468.

16 even divisors

2, 6, 10, 14, 30, 42, 50, 70, 150, 210, 250, 350, 750, 1050, 1750, 5250

16 odd divisors

1, 3, 5, 7, 15, 21, 25, 35, 75, 105, 125, 175, 375, 525, 875, 2625

How to compute the divisors of 5250?

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 5250 by each of the numbers from 1 to 5250 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)

5250 / 1 = 5250 (the remainder is 0, so 1 is a divisor of 5250)
5250 / 2 = 2625 (the remainder is 0, so 2 is a divisor of 5250)
5250 / 3 = 1750 (the remainder is 0, so 3 is a divisor of 5250)
...
5250 / 5249 = 1.0001905124786 (the remainder is 1, so 5249 is not a divisor of 5250)
5250 / 5250 = 1 (the remainder is 0, so 5250 is a divisor of 5250)

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 5250 (i.e. 72.456883730947). 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 $\frac{N}{d} = D$ )

5250 / 1 = 5250 (the remainder is 0, so 1 and 5250 are divisors of 5250)
5250 / 2 = 2625 (the remainder is 0, so 2 and 2625 are divisors of 5250)
5250 / 3 = 1750 (the remainder is 0, so 3 and 1750 are divisors of 5250)
...
5250 / 71 = 73.943661971831 (the remainder is 67, so 71 is not a divisor of 5250)
5250 / 72 = 72.916666666667 (the remainder is 66, so 72 is not a divisor of 5250)