Question

How do you write the prime factorization of 48?

Answer 1

Hint: The factors are those numbers which can completely divide the given number. They can be positive and negative. The method of obtaining the factors of the numbers is known as the prime factorization method. Check all the numbers and take out the numbers which are completely 48.

Complete Step by Step Solution:
The prime factorization method can be defined as the method which is used for obtaining the factors of the given number. In the prime factorization method, the number is divided by every possible number that can divide the given number completely.
Factors of the number are those numbers that can completely divide the given number. In other words, we can also say that factors are those which when divided the number gives remainder as 0. By multiplying the factors, we can also get another number. There are many numbers that have more than one factorization. For example, the number 12 can be factored as \[1 \times 12\] or $2 \times 6$ or $4 \times 3$.
From the question, we know that we have to do the prime factorization of the number 48. We can also say that we have to find the factors of 48. Therefore, we know that 48 is an even number.
So, now let us simply divide the given number 48 by every possible number that can completely divide 48 –
$
  48 \div 1 = 48 \\
  48 \div 2 = 24 \\
  48 \div 3 = 16 \\
  48 \div 4 = 12 \\
  48 \div 6 = 8 \\
  48 \div 8 = 6 \\
  48 \div 12 = 4 \\
  48 \div 16 = 3 \\
  48 \div 24 = 2 \\
  48 \div 48 = 1 \\
 $
From the above, we can conclude that the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.
For the prime factorization of 48, we can write it as –
$
  48 \div 2 = 24 \\
  24 \div 2 = 12 \\
  12 \div 2 = 6 \\
  6 \div 2 = 3 \\
  3 \div 3 = 1 \\
 $
So, the prime factorization of 48 is $2 \times 2 \times 2 \times 2 \times 3$
$2 \times 2 \times 2 \times 2 \times 3$ can also be written as –
$ \Rightarrow {2^4} \times 3$

Hence, the prime factorization of 48 is ${2^4} \times 3$.

Note:
The steps to find the prime factorization of the number is:
1) The first step is dividing the given number with the smallest prime factor.
2) Now, check whether the next number will be divided by the prime factor in step 1 otherwise move on to the next prime factor.
3) Repeat the same until you get 1 at the end.