Questions: How many natural numbers less than 200 are divisible by 4, but not divisible by 3?

Solution Steps

To solve this problem, we need to find natural numbers less than 200 that are divisible by 50 and 4, but not divisible by 3. First, determine the least common multiple (LCM) of 50 and 4 to find numbers divisible by both. Then, list these numbers and filter out those divisible by 3.

To find natural numbers less than 200 that are divisible by both 50 and 4, we first calculate the least common multiple (LCM) of 50 and 4. The LCM can be calculated as follows:

\[ \text{lcm}(50, 4) = \frac{50 \times 4}{\text{gcd}(50, 4)} = 100 \]

Next, we identify the multiples of 100 that are less than 200. The multiples of 100 below 200 are:

\[ 100, 200 \]

However, since we are looking for numbers less than 200, we only consider:

\[ 100 \]

Now, we need to check if the identified number (100) is divisible by 3. We perform the division:

\[ 100 \div 3 \approx 33.33 \]

Since 100 is not an integer multiple of 3, it is not divisible by 3.

Final Answer