What are the divisors of 1482?

1, 2, 3, 6, 13, 19, 26, 38, 39, 57, 78, 114, 247, 494, 741, 1482

There is a total of 16 positive divisors.
The sum of these divisors is 3360.
The arithmetic mean is 210.

8 even divisors

2, 6, 26, 38, 78, 114, 494, 1482

8 odd divisors

1, 3, 13, 19, 39, 57, 247, 741

How to compute the divisors of 1482?

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 1482 by each of the numbers from 1 to 1482 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)

1482 / 1 = 1482 (the remainder is 0, so 1 is a divisor of 1482)
1482 / 2 = 741 (the remainder is 0, so 2 is a divisor of 1482)
1482 / 3 = 494 (the remainder is 0, so 3 is a divisor of 1482)
...
1482 / 1481 = 1.0006752194463 (the remainder is 1, so 1481 is not a divisor of 1482)
1482 / 1482 = 1 (the remainder is 0, so 1482 is a divisor of 1482)

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 1482 (i.e. 38.49675310984). 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 $\frac{N}{d} = D$ )

1482 / 1 = 1482 (the remainder is 0, so 1 and 1482 are divisors of 1482)
1482 / 2 = 741 (the remainder is 0, so 2 and 741 are divisors of 1482)
1482 / 3 = 494 (the remainder is 0, so 3 and 494 are divisors of 1482)
...
1482 / 37 = 40.054054054054 (the remainder is 2, so 37 is not a divisor of 1482)
1482 / 38 = 39 (the remainder is 0, so 38 and 39 are divisors of 1482)