I do not understand this problem can somebody please help me with it? Fill in the missing digits in as many ways as possible so the number will be divisible by 6.
3 _ 2 _ Thanks for the help.
As you already know, For the number to be divisible, it has to be divisible by 2 and by 3.
Divisble by 2 means that the last digit must be even (2,4,6,8,0).
Divisible by three means that the sum of the digits must add up to a multiple of 3.
So start with the last digit as 2, and fill in the second digit with all possible answers (2,5,8).
Repeat the same using 4 as the last digit, and find the possible answers for the second digit (3, 6, 9).
Now repeat 6,8,0 successively for the last digit and repeat the above.
You should have a total of 5*3=15 numbers.
I have a total of 16 numbers not 15 and I have double checked my answers
Of course! To find the missing digits in order to make the number divisible by 6, we need to understand the divisibility rule for 6. A number is divisible by 6 if it is divisible by both 2 and 3.
First, let's focus on divisibility by 2. A number is divisible by 2 if its last digit is an even number (0, 2, 4, 6, or 8). In our case, we have a blank space where a digit needs to be. Since any even number can be used, we have many options. We can fill in the blank with any of the digits {0, 2, 4, 6, or 8}.
Now, let's consider divisibility by 3. A number is divisible by 3 if the sum of its digits is also divisible by 3. In our case, we have two blank spaces where digits need to be filled. We need to choose the digits in a way that the sum of all the digits is divisible by 3.
To fill in the blanks, we can try all possible combinations of digits for the two spaces. Let's start with the first blank space, which can be any number from 0 to 9. Once we choose a digit for the first space, we can determine the possible digits for the second space by using the rule of divisibility by 3.
For example, if we choose 3 for the first space, we need to find a digit for the second space such that the sum {3 + digit} is divisible by 3. We can try all possible digits (from 0 to 9) and check their sums with 3 to see which combinations give a sum divisible by 3.
Once we have all the possible combinations, we can check each of them by substituting the digits back into the number (3 _ 2 _) and see if the resulting number is divisible by 6. If it is, then we have found a valid combination.
By following this process and trying all possible combinations, we can find the missing digits to make the number divisible by 6.