How many positive three-digit integers with each digit greater than 4 are divisible by 6??
It is 16. Just list all the cases
12 is wrong
Why did the math book go to the comedy club? Because it wanted to learn some funny divisions! Now, let's solve this problem with a smile.
To find positive three-digit integers with each digit greater than 4 that are divisible by 6, we need to consider two conditions: being a three-digit integer and being divisible by 6.
First, let's see how many three-digit integers can be formed with digits greater than 4. Well, there are 5 digits greater than 4, which are 5, 6, 7, 8, and 9. So, we have 5 options for each of the three digits, giving us a total of 5 × 5 × 5 = 125 possible three-digit numbers.
Now, let's figure out how many of these are divisible by 6. A number is divisible by 6 if it is divisible by both 2 and 3. Since any number divisible by 3 must have a sum of digits divisible by 3, we can narrow down our options.
For the sum of digits to be divisible by 3, we need to choose the digits in a way that their sum is a multiple of 3. Since all the digits greater than 4 are odd numbers, their sum will always be odd. Therefore, none of these three-digit numbers will be divisible by 3.
As a result, we have zero three-digit integers greater than 4 that are divisible by 6. But hey, at least we had a good laugh along the way!
Why don't mathematicians throw house parties? Because too many numbers would show up uninvited!
To find the number of positive three-digit integers that are divisible by 6 and have each digit greater than 4, we can break down the problem into several steps:
Step 1: Determine the possible values for the units digit.
Since the units digit must be greater than 4 and divisible by 2, the possible values are 6, 8, which are greater than 4 and divisible by 2.
Step 2: Determine the possible values for the tens digit.
Since the tens digit must be greater than 4 and divisible by 3, we can analyze each possible value of the units digit and find the corresponding valid tens digit:
- If the units digit is 6, there is no tens digit greater than 4 and divisible by 3.
- If the units digit is 8, the only valid tens digit is 5.
Step 3: Determine the possible values for the hundreds digit.
Since the hundreds digit must be greater than 4, there are 6 possible values: 5, 6, 7, 8, 9.
Step 4: Calculate the total number of valid three-digit integers.
To find the total number of valid three-digit integers, we multiply the number of possibilities for each digit:
- For the units digit, there are 2 possibilities (6 and 8)
- For the tens digit, there is only 1 possibility (5)
- For the hundreds digit, there are 5 possibilities (5, 6, 7, 8, 9)
Total number of valid three-digit integers = 2 * 1 * 5 = 10
Therefore, there are 10 positive three-digit integers with each digit greater than 4 that are divisible by 6.
From your description, the numbers can only contain 5, 6, 7, 8 and/or 9.
You can start with 666, 678 and go to 996.