number less than 200 sum of the digit is 6 product of the digit is 0 each factor of 75 is its factor too?

yes

I'd say no.

The prime factors of 75 are 3 and 5
All the factors of 75 are 3,5,15,25

Write n = abc

Since the product of the digits is zero, one of the digits is zero.

Since the sum of the digits is 6, the number is 9k+6 for some k.

That means that 3 is a factor of n

Now, abc is either

105 or 150

3,5,15 are factors of both. 25 does not divide 105.

To find a number that is less than 200, has a digit sum of 6, and a digit product of 0, we can follow these steps:

1. Start by listing down all the numbers less than 200.

2. For each number, calculate the sum of its digits and check if it equals 6.

3. If the sum of the digits is 6, calculate the product of its digits and check if it equals 0.

4. Lastly, check if each factor of the number is also a factor of 75.

Let's go through each step:

Step 1: List down numbers less than 200:
The numbers less than 200 are 1, 2, 3, ..., 197, 198, 199.

Step 2: Calculate the sum of the digits:
Let's take the number 123 as an example.
The sum of its digits is 1 + 2 + 3 = 6.

Step 3: Calculate the product of the digits:
The product of the digits of the number 123 is 1 * 2 * 3 = 6.

Step 4: Check if each factor is also a factor of 75:
For example, if we have the number 12, which is a factor of 75, we need to check if both 1 and 2 are factors of 75. If they are, then the number satisfies this condition.

By following these steps, you can go through each number less than 200, check if both the digit sum and digit product conditions are satisfied, and verify if each factor is also a factor of 75.