What are the divisors of 1464?

1, 2, 3, 4, 6, 8, 12, 24, 61, 122, 183, 244, 366, 488, 732, 1464

There is a total of 16 positive divisors.
The sum of these divisors is 3720.
The arithmetic mean is 232.5.

12 even divisors

2, 4, 6, 8, 12, 24, 122, 244, 366, 488, 732, 1464

4 odd divisors

1, 3, 61, 183

How to compute the divisors of 1464?

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 1464 by each of the numbers from 1 to 1464 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)

1464 / 1 = 1464 (the remainder is 0, so 1 is a divisor of 1464)
1464 / 2 = 732 (the remainder is 0, so 2 is a divisor of 1464)
1464 / 3 = 488 (the remainder is 0, so 3 is a divisor of 1464)
...
1464 / 1463 = 1.0006835269993 (the remainder is 1, so 1463 is not a divisor of 1464)
1464 / 1464 = 1 (the remainder is 0, so 1464 is a divisor of 1464)

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 1464 (i.e. 38.262252939418). 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 $\frac{N}{d} = D$ )

1464 / 1 = 1464 (the remainder is 0, so 1 and 1464 are divisors of 1464)
1464 / 2 = 732 (the remainder is 0, so 2 and 732 are divisors of 1464)
1464 / 3 = 488 (the remainder is 0, so 3 and 488 are divisors of 1464)
...
1464 / 37 = 39.567567567568 (the remainder is 21, so 37 is not a divisor of 1464)
1464 / 38 = 38.526315789474 (the remainder is 20, so 38 is not a divisor of 1464)