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**Hint:**In this question, we have a number and find the prime factor of a given number. In this question to find the prime factor of a given number, we used the prime factorization method. According to the prime factorization method, we divide the given number with the least prime number and leave no reminder. Again, we divided the produced quotient by the least prime number, and we repeated this step until the quotient came as \[1\].

**Complete step by step answer:**

Now we come to the question. From the question, the number is given as below.

\[{\text{number}} = 144\]

We used the prime factorization method to find the prime factors of a given number.

According to the prime factorization method, we divided the given number with the least prime number with no reminder. Again we divided the produced quotient by least number. It is repeated up to when the quotient is produced as \[1\].

Now, the least prime number is \[2\]. We divided the given number by that prime number.

Then,

\[ \Rightarrow \dfrac{{144}}{2} = 72\]

Here the prime factor is \[2\] and the quotient is \[72\].

Then,

\[ \Rightarrow \dfrac{{72}}{2} = 36\]

Here the prime factor is \[2\] and the quotient is \[36\].

Then,

\[ \Rightarrow \dfrac{{36}}{2} = 18\]

Here the prime factor is \[2\] and the quotient is \[18\].

Then,

\[ \Rightarrow \dfrac{{18}}{2} = 9\]

Here the prime factor is \[2\] and the quotient is\[9\].

When we divided the \[9\] by \[2\] then there was a reminder.

Then, we select the next prime number. The next prime number is \[3\].

Hence,

\[ \Rightarrow \dfrac{9}{3} = 3\]

Here the prime number is \[3\] and the quotient is \[3\].

Then,

\[ \Rightarrow \dfrac{3}{3} = 1\]

Here the prime number is \[3\] and the quotient is \[1\].

**Therefore, the prime factorization of \[144\] are \[2 \times 2 \times 2 \times 2 \times 3 \times 3\].**

**Note:**

In this question, we used the word prime number. Prime number is defined as the number which has only two factors that is \[1\] and itself while the factors are defined as the numbers which are multiplied to get another number. Now we know about what prime factors are. Prime factors are defined as a factor which is prime number and not a composite number.

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