Question

Find the H.C.F. of the given set of numbers. The numbers are 48, 24, 72.

Answer 1

Hint: The H.C.F. is found by first finding the factors and then taking out the greatest factors that are common for the given set of numbers.

Complete step-by-step solution -
In this question, we have to find the H.C.F. of the numbers 48, 24, 72.
So the first step will be prime factorization of each number. In other words, factorize each number.
So we have:
\[\begin{align}
  & 48=2\times 2\times 2\times 2\times 3 \\
 & 24=2\times 2\times 2\times 3 \\
 & 72=2\times 2\times 2\times 3\times 3 \\
\end{align}\]
Next we will take the common factors from each, as follows:
\[\begin{align}
  & 48=\fbox{2} \times\fbox{2} \times \fbox{2} \times 2 \times \fbox{3} \\
 & 24=\fbox{2} \times\fbox{2} \times \fbox{2} \times \fbox{3} \\
 & 72=\fbox{2} \times\fbox{2} \times \fbox{2} \times \fbox{3} \times 3 \\
\end{align}\]
Now, all the numbers that are in the box are common in all three. So, now we will take out these factors and multiply to get the H.C.F., as follows:
H.C.F= \[2\times 2\times 2\times 3=24\]
Finally the H.C.F. of 48, 24, 72 is 24.

Note: To find the HCF, the best way will be to find the prime factorization of all the given set of numbers and the product of common factors is the HCF. It is to be kept in mind that we multiply all the common factors just once to get the HCF.