Ratio of two numbers are 2:3 and their H.C.F is 15. Find the numbers.

Given that the ratio of two numbers is \( 2:3 \) and their highest common factor (HCF) is 15, we can represent the numbers in terms of their ratio as follows:

Let the two numbers be:
- \( 2x \) and \( 3x \), where \( x \) is a common factor.

Since the HCF of the two numbers is given as 15, and \( 2 \) and \( 3 \) are co-prime (they have no common factor other than 1), \( x \) must be equal to the HCF. Therefore, \( x = 15 \).

Now, substitute \( x = 15 \) into the expressions for the two numbers:

- First number: \( 2x = 2 \times 15 = 30 \)
- Second number: \( 3x = 3 \times 15 = 45 \)

Thus, the two numbers are **30** and **45**.

---

Would you like more details or explanations on any part of this process?

Here are 5 related questions for further exploration:

1. How do you find the HCF of two numbers?
2. What is the difference between the HCF and the LCM?
3. Can two numbers with a ratio of 4:5 have an HCF of 12? Why or why not?
4. How would the solution change if the ratio were 5:7 and the HCF was 10?
5. What is the significance of co-prime numbers in determining HCF?

**Tip:** The HCF of two numbers is always a factor of both numbers, while their least common multiple (LCM) is a multiple of both numbers.

Learn how to find two numbers given their ratio 2:3 and their HCF as 15. This problem covers key concepts of ratios and greatest common divisor, providing a step-by-step solution. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation