What are the divisors of 1488?

1, 2, 3, 4, 6, 8, 12, 16, 24, 31, 48, 62, 93, 124, 186, 248, 372, 496, 744, 1488

There is a total of 20 positive divisors.
The sum of these divisors is 3968.
The arithmetic mean is 198.4.

16 even divisors

2, 4, 6, 8, 12, 16, 24, 48, 62, 124, 186, 248, 372, 496, 744, 1488

4 odd divisors

1, 3, 31, 93

How to compute the divisors of 1488?

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 1488 by each of the numbers from 1 to 1488 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)

1488 / 1 = 1488 (the remainder is 0, so 1 is a divisor of 1488)
1488 / 2 = 744 (the remainder is 0, so 2 is a divisor of 1488)
1488 / 3 = 496 (the remainder is 0, so 3 is a divisor of 1488)
...
1488 / 1487 = 1.0006724949563 (the remainder is 1, so 1487 is not a divisor of 1488)
1488 / 1488 = 1 (the remainder is 0, so 1488 is a divisor of 1488)

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 1488 (i.e. 38.574603043972). 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 $\frac{N}{d} = D$ )

1488 / 1 = 1488 (the remainder is 0, so 1 and 1488 are divisors of 1488)
1488 / 2 = 744 (the remainder is 0, so 2 and 744 are divisors of 1488)
1488 / 3 = 496 (the remainder is 0, so 3 and 496 are divisors of 1488)
...
1488 / 37 = 40.216216216216 (the remainder is 8, so 37 is not a divisor of 1488)
1488 / 38 = 39.157894736842 (the remainder is 6, so 38 is not a divisor of 1488)