Question

Find the HCF of: 16 and 24.

Answer 1

Hint: In this problem, we need to find the factors of 16 and 24 which divide them without leaving a remainder. Now, find the common factors of 16 and 24. Then, find the highest common factor.

Complete step by step answer:
The factors of 16 are shown below.
\[\begin{aligned}
  \,\,\,\,\,\,16 = 16 \times 1 \\
   \Rightarrow 16 = 8 \times 2 \\
   \Rightarrow 16 = 4 \times 4 \\
\end{aligned}\]
The list of the factors of 16 which divide 16 without leaving a remainder is shown below.
\[16 = \left\{ {1,2,4,8,16} \right\}\]
The factors of 24 are shown below.
\[\begin{aligned}
  \,\,\,\,\,\,24 = 24 \times 1 \\
   \Rightarrow 24 = 12 \times 2 \\
   \Rightarrow 24 = 8 \times 3 \\
   \Rightarrow 24 = 6 \times 4 \\
\end{aligned}\]
The list of the factors of 24 which divide 24 without leaving a remainder is shown below.
\[24 = \left\{ {1,2,3,4,6,8,12,24} \right\}\]
Now, the common factors of 16 and 24 which divide 16 and 24 without living a denominator is the intersection of the above two factors.
\[{\text{common factors = }}\left\{ {1,2,4,8} \right\}\]
The highest common factor is 8, therefore,
\[HCF\left( {16,24} \right) = 8\]

Thus, the HCF of 16 and 24 is 8.

Note: The HCF of the two numbers represents the highest common factor existing between them. We can obtain the HCF of the given integers with the help of the prime factorization method and long division method also. The HCF of two prime numbers is 1.