The HCF of 17.5 , 42 and 14 is _________.

The HCF of 17.5, 42, and 14

Convert all numbers to the same form (either all integers or all decimals) and then find the HCF.

To simplify calculations, we eliminate the decimal in 17.5

​$$17.5=\frac{175}{10}=\frac{35}{2}$$​​

Now we are working with the following numbers:

$$\frac{5}{2}, 42, \text { and } 14$$​​

To make comparison easier, express all numbers with a common denominator:

​$$\begin{aligned}& \frac{35}{2}=\frac{35}{2} \text { (no change) } \\& 42=\frac{42}{1}=\frac{84}{2} \\& 14=\frac{14}{1}=\frac{28}{2}\end{aligned}$$​​

So the numbers become:

​$$\frac{35}{2}, \frac{84}{2}, \frac{28}{2}$$ 

Now we calculate the HCF of the numerators: 35, 84 and 28

Prime factorizations:

$$\begin{aligned}& 35=5 \times 7 \\& 84=2^2 \times 3 \times 7 \\& 28=2^2 \times 7\end{aligned}$$ 

The common factor among all numerators is 7.

Since the denominators are the same (222), 

So, HCF = $$7\div2=3.5$$​