Question

Establish a divisibility rule for 6. Based on the said rule, verify if the number 1790184 is divisible by 6.

Answer 1

For a given number to be divisible by another number, the given number should be a multiple to all the factors of the latter.
Therefore, for a number to be exactly divisible by 6, it must also be simultaneosly divisible by its factors.
6 = 6 $\times$ 1
6 = 2 $\times$ 3
So factors of 6 are: 1, 2, 3 and 6.

So the number should be divisible by 2 and 3 simultaneously, for it to be divisible by 6.

Applying the above divisibility rule, we get
1790184 $\to$ Divisible by 2 as its units place is an even number.
$\to$ Divisible by 3 as sum of its digits (= 30) is divisible by 3.
Since the number is divisible by both 2 and 3, therefore, it is divisible by 6.