Certainly! Let's solve this step-by-step.
Given:
- The HCF (Highest Common Factor) of two numbers is 145.
- The LCM (Least Common Multiple) of the same two numbers is 2175.
- One of the numbers is 725.
We need to find the other number.
To do this, we'll use the relationship between HCF, LCM, and the two numbers:
[tex]\[ \text{HCF} \times \text{LCM} = \text{number1} \times \text{number2} \][/tex]
Given:
[tex]\[ \text{HCF} = 145 \][/tex]
[tex]\[ \text{LCM} = 2175 \][/tex]
[tex]\[ \text{number1} = 725 \][/tex]
Let's denote the unknown number as [tex]\(\text{number2}\)[/tex].
We can rearrange the formula to solve for [tex]\(\text{number2}\)[/tex]:
[tex]\[ \text{number2} = \frac{\text{HCF} \times \text{LCM}}{\text{number1}} \][/tex]
Now substitute the given values into the equation:
[tex]\[ \text{number2} = \frac{145 \times 2175}{725} \][/tex]
From calculation,
[tex]\[ \text{number2} = 435.0 \][/tex]
So, the other number is:
[tex]\[ \boxed{435} \][/tex]
