Numbers Finder by Ratio and HCF

Input the ratio and HCF of two numbers to quickly calculate their actual values.

Calculate Two Numbers Using Their Ratio and HCF

Result

How to Calculate Two Numbers Using Their Ratio and HCF

Suppose the two numbers are \( x \) and \( y \), and their ratio is \( r_1 : r_2 \), with the highest common factor \( \text{HCF} \) given.

Steps

1. Understand the ratio

Assume the two numbers can be expressed as: \( x = k \cdot r_1, \quad y = k \cdot r_2 \) Here, \( k \) is a proportional coefficient. The ratio between the numbers is \( r_1 : r_2 \).

2. Determine the HCF

Since \( \text{HCF}(x, y) = k \cdot \text{HCF}(r_1, r_2) \), the proportional coefficient \( k \) can be calculated as: \( k = \frac{\text{HCF}}{\text{HCF}(r_1, r_2)} \)

3. Find \( x \) and \( y \)

Substitute \( k \) into the expressions for \( x \) and \( y \): \( x = k \times r_1 \) \( y = k \times r_2 \)

Examples

Example 1: The ratio of two numbers is 11:15 and their HCF is 13, find the two numbers.

Solution:

1. Compute the HCF:

\( \text{HCF}(11, 15) = 1 \)

2. Compute the proportional coefficient \( k \):

\( k = \frac{13}{1} = 13 \)

3. Substitute \( k \) into the formulas for \( x \) and \( y \):

\( x = 13 \times 11 = 143 \)

\( y = 13 \times 15 = 195 \)

Result: The two numbers are 143 and 195.

Example 2: The ratio of two numbers is 3:4 and their HCF is 15, find the two numbers.

Solution:

1. Compute the HCF:

\(\text{HCF}(3, 4) = 1 \)

2. Compute the proportional coefficient \( k \):

\( k = \frac{15}{1} = 15 \)

3. Substitute \( k \) into the formulas for \( x \) and \( y \):

\( x = 15 \times 3 = 45 \)

\( y = 15 \times 4 = 60 \)

Result: The two numbers are 45 and 60.