Question

Find the HCF of the following’
612,816 and 448.

Answer 1

Hint: HCF is called the highest common factor. It is the greatest number which can divide the given numbers. It is the numbers which are common in all three numbers. HCF is also called the greatest common divisor that is GCD.

Complete step-by-step answer:
Let's understand the definition of HCF. HCF is the highest common factor. It means the greatest number which can divide the given numbers.
HCF is also known as the greatest common divisor (GCD).
Here, we need to find the factors of all the numbers above numbers given.
Let's start with the first number that is 612.
$\begin{align}
  & \left. {\underline {\,
 2 \,}}\! \right| 612 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 306 \\
 & \left. {\underline {\,
 3 \,}}\! \right| 153 \\
 & \left. {\underline {\,
 3 \,}}\! \right| 51 \\
 & \left. {\underline {\,
 17 \,}}\! \right| 17 \\
\end{align}$
Therefore, the factors of number 612 are $612=2\times 2\times 3\times 3\times 17$ .
Let's start with the second number that is 816.
$\begin{align}
  & \left. {\underline {\,
 2 \,}}\! \right| 816 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 408 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 204 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 102 \\
 & \left. {\underline {\,
 3 \,}}\! \right| 51 \\
 & \left. {\underline {\,
 17 \,}}\! \right| 17 \\
\end{align}$
Therefore, the factors of number 816 are $816=2\times 2\times 2\times 2\times 2\times 3\times 17$ .
Let's start with the third number that is 448.
$\begin{align}
  & \left. {\underline {\,
 2 \,}}\! \right| 448 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 224 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 112 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 56 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 28 \\
 & \left. {\underline {\,
 2 \,}}\! \right| 14 \\
 & \left. {\underline {\,
 7 \,}}\! \right| 7 \\
\end{align}$
Therefore, the factors of number 448 are $448=2\times 2\times 2\times 2\times 2\times 2\times 7$ .
Now, we need to find the factors that are common in the above three numbers.
We can see that the factors common here are $2\times 2=4$ .
Therefore, the HCF of the numbers 612,816 and 448 is 4.

Note: We need to find the factors that are common in all the three numbers and not only in two numbers. Also, we need to understand that the HCF and GCD (Greatest common divisor) are the same. Therefore, the GCD of 612,816 and 448 is 4.