The product of two numbers is 700 that LCM is 700 find the HCF

To solve this problem, we use the relationship between the product of two numbers, their LCM (Least Common Multiple), and their HCF (Highest Common Factor).

### Given:
1. The product of two numbers is \(700\).
2. The LCM of the two numbers is \(700\).

### Formula:
The relationship between the product of two numbers, their LCM, and their HCF is given by:

\[
\text{Product of two numbers} = \text{LCM} \times \text{HCF}
\]

Let's denote the two numbers by \(a\) and \(b\), their LCM by \(\text{LCM}(a, b) = 700\), and their HCF by \(\text{HCF}(a, b) = x\). According to the formula:

\[
a \times b = \text{LCM}(a, b) \times \text{HCF}(a, b)
\]

Substitute the given values:

\[
700 = 700 \times x
\]

To find \(x\), divide both sides by 700:

\[
x = \frac{700}{700} = 1
\]

### Conclusion:
The HCF of the two numbers is **1**.

Would you like more details or have any questions? Here are 5 related questions you might consider:

1. What is the relationship between the GCD (Greatest Common Divisor) and the HCF?
2. How can you find the LCM and HCF of two numbers using their prime factorization?
3. If the HCF of two numbers is 1, what does that tell us about the numbers?
4. How does the Euclidean algorithm help in finding the HCF of two numbers?
5. What are some real-life applications where finding the LCM or HCF is necessary?

**Tip:** When two numbers have an HCF of 1, they are considered "coprime," meaning they share no common factors other than 1.

Discover how to find the Highest Common Factor (HCF) of two numbers when given their product and LCM. This math problem explores arithmetic and number theory concepts, suitable for Grades 5-7 students.

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