Question

What is the prime factorization of \[48\]?

Answer 1

Hint: The prime factorization of \[48\] can be done by dividing \[48\] with any of the prime number by which \[48\] is divisible in every step until \[1\] or any prime number is obtained. By performing the prime factorization, we can obtain the prime numbers that divide\[48\].

Complete step-by-step answer:
Let us have brief information regarding prime factorization.
Prime factorization is performed upon composite numbers to find the prime factors of the certain composite number. We have two common methods of performing prime factorization. They are factor tree method and upside down division. We make use of this method to break down the number into primes so as to express them as a product of primes. If there occurs a single prime factor of a number multiple times, then we can express them in exponential form.
Now let us perform prime factorization for \[48\] by upside down division.
\[\begin{align}
  & 2\left| \!{\underline {\,
  48 \,}} \right. \\
 & 2\left| \!{\underline {\,
  24 \,}} \right. \\
 & 2\left| \!{\underline {\,
  12 \,}} \right. \\
 & 2\left| \!{\underline {\,
  6 \,}} \right. \\
 & \left| \!{\underline {\,
  3 \,}} \right. \\
\end{align}\]
The common prime factors of \[48\] are \[2\] and \[3\].
This can be written as \[48=2\times 2\times 2\times 2\times 3\]
It can be expressed in exponential form as \[{{2}^{4}}\times 3\].

Note: We can perform this prime factorization of a composite number to list out the prime numbers that divide them as well as it can be used to find the LCM and HCF or certain pairs of numbers. The prime factorization of a prime number can also be done, but the prime factor that divides the number would be the number itself.