To find the other number when the HCF (Highest Common Factor) of two numbers is 16, their LCM (Least Common Multiple) is 160, and one of the numbers is 80, we can use the relationship between HCF, LCM, and the two numbers. The relationship is given by the formula:
[tex]\[ \text{HCF} \times \text{LCM} = \text{num1} \times \text{num2} \][/tex]
Given:
- HCF ([tex]\( \text{hcf} \)[/tex]) = 16
- LCM ([tex]\( \text{lcm} \)[/tex]) = 160
- One number ([tex]\( \text{num1} \)[/tex]) = 80
We need to find the other number ([tex]\( \text{num2} \)[/tex]).
Substituting the given values into the formula:
[tex]\[ 16 \times 160 = 80 \times \text{num2} \][/tex]
Next, simplify the left side of the equation:
[tex]\[ 2560 = 80 \times \text{num2} \][/tex]
To isolate [tex]\( \text{num2} \)[/tex], divide both sides of the equation by 80:
[tex]\[ \text{num2} = \frac{2560}{80} \][/tex]
Perform the division:
[tex]\[ \text{num2} = 32 \][/tex]
Hence, the other number is:
[tex]\[ \boxed{32} \][/tex]
So, the correct answer is:
a. 32
