An unknown number and 42 has a GCF of 6 and has a LCM of 210, What is the unknown number?

Let's denote the unknown number as \( x \).

We are given:
- The greatest common factor (GCF) of \( x \) and 42 is 6.
- The least common multiple (LCM) of \( x \) and 42 is 210.

There is a relationship between the GCF, LCM, and the two numbers involved, given by the formula:

\[
\text{GCF}(x, 42) \times \text{LCM}(x, 42) = x \times 42
\]

Substituting the known values:

\[
6 \times 210 = x \times 42
\]

Simplifying the left side:

\[
1260 = x \times 42
\]

Now, solve for \( x \):

\[
x = \frac{1260}{42} = 30
\]

Thus, the unknown number is \( \boxed{30} \).

Would you like more details or have any questions? 

Here are some related questions:
1. What is the general formula connecting GCF and LCM with two numbers?
2. How do you find the GCF of two numbers?
3. How can you compute the LCM of two numbers?
4. What would happen if the GCF and LCM of two numbers were the same?
5. How do we verify if 30 is the correct number here?

**Tip:** You can verify your result by checking both the GCF and LCM after solving to ensure they match the problem's conditions.

An unknown number and 42 has a GCF of 6 and has a LCM of 210. What is the unknown number?

Learn how to find the unknown number when given the GCF (6) and LCM (210) with a step-by-step solution. This problem involves key number theory concepts such as GCF, LCM, and the relationship between them. Ideal for students in Grades 6-8.

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