What are the divisors of 1512?

1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 18, 21, 24, 27, 28, 36, 42, 54, 56, 63, 72, 84, 108, 126, 168, 189, 216, 252, 378, 504, 756, 1512

There is a total of 32 positive divisors.
The sum of these divisors is 4800.
The arithmetic mean is 150.

24 even divisors

2, 4, 6, 8, 12, 14, 18, 24, 28, 36, 42, 54, 56, 72, 84, 108, 126, 168, 216, 252, 378, 504, 756, 1512

8 odd divisors

1, 3, 7, 9, 21, 27, 63, 189

How to compute the divisors of 1512?

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 1512 by each of the numbers from 1 to 1512 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)

1512 / 1 = 1512 (the remainder is 0, so 1 is a divisor of 1512)
1512 / 2 = 756 (the remainder is 0, so 2 is a divisor of 1512)
1512 / 3 = 504 (the remainder is 0, so 3 is a divisor of 1512)
...
1512 / 1511 = 1.0006618133686 (the remainder is 1, so 1511 is not a divisor of 1512)
1512 / 1512 = 1 (the remainder is 0, so 1512 is a divisor of 1512)

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 1512 (i.e. 38.884444190447). 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 $\frac{N}{d} = D$ )

1512 / 1 = 1512 (the remainder is 0, so 1 and 1512 are divisors of 1512)
1512 / 2 = 756 (the remainder is 0, so 2 and 756 are divisors of 1512)
1512 / 3 = 504 (the remainder is 0, so 3 and 504 are divisors of 1512)
...
1512 / 37 = 40.864864864865 (the remainder is 32, so 37 is not a divisor of 1512)
1512 / 38 = 39.789473684211 (the remainder is 30, so 38 is not a divisor of 1512)