Question

What are all the factor pairs of $192$?

Answer 1

Hint: In this question, we need to find the factor pairs of $192$. So, we will find out the prime factors of the given number using the prime factorisation method and then find all the factor pairs by multiplying the prime factors with each other.

Complete step-by step answer:
Here, we need to find the factor pairs of $192$.
We know that $192$ is a composite number.
So, we will first find out all the prime factors of the number using the prime factorization. So, we get,
\[\begin{align}
  & 2\left| \!{\underline {\,
  192 \,}} \right. \\
 & 2\left| \!{\underline {\,
  96 \,}} \right. \\
 & 2\left| \!{\underline {\,
  48 \,}} \right. \\
 & 2\left| \!{\underline {\,
  24 \,}} \right. \\
 & 2\left| \!{\underline {\,
  12 \,}} \right. \\
 & 2\left| \!{\underline {\,
  6 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3 \,}} \right. \\
\end{align}\]
So, the prime factorisation of the number $192$ is: $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3$
$ = {2^6} \times {3^1}$
Now, we will find the possible factor pairs of the number $192$ by multiplying the prime factors with each other.
Therefore, the possible factors of $192$ are: $192$, $96$, $64$, $48$, $32$, $24$, $16$,$12$, $8$, $6$, $4$, $3$, $2$, $1$.
Hence, the factor pairs of $192$ are: $192 \times 1$, $96 \times 2$, $48 \times 4$, $24 \times 8$, $12 \times 16$, $6 \times 32$,$3 \times 64$.

Note:
Prime factorization is a method of finding prime numbers which multiply to make the original number. A prime number is a natural number greater than $1$ that is not a product of two smaller natural numbers. In prime factorization, we start dividing the number by the first prime number $2$ and continue to divide by $2$ until we get a decimal or remainder. Then divide by $3,5,7,....$etc. until we get the remainder $1$ with the factors as prime numbers. Then write the numbers as a product of prime numbers.