Question

What is the prime factorization of \[180\]?

Answer 1

Hint: To find the answer to the question given above, divide \[180\] by just prime numbers to find the prime factorization. Prime numbers are whole numbers greater than \[1\] that can only be divided equally by themselves and \[1\]. Also, remember a composite number is a real number greater than \[1\] that is not prime.

Complete step-by-step answer:
We have to find prime factorization of \[180\]
Now, we know Factorization, also known as factoring, is the process of writing a number or another mathematical entity as a result of many variables, which are usually smaller or simpler objects of the same nature.
We have to find the answer through prime factorization.
Now,
Divide \[180\] by the lowest prime number \[{\text{2}}\], then repeat until it can no longer be divided by \[{\text{2}}\], then pass on to the next prime number \[{\text{3}}\] , and so on. We have our prime factors where the remainder is \[{\text{1}}\].
Now, first divide \[180\] by lowest prime number \[{\text{2}}\], we get:
\[
  180 \div 2 = 90 \\
   \Rightarrow 90 \div 2 = 45 \\
 \]
Now, divide this by \[{\text{3}}\], we get:
\[
  45 \div 3 = 15 \\
   \Rightarrow 15 \div 3 = 5 \\
 \]
Now, divide it by \[5\]. We get:
\[5 \div 5 = 1\], we have reached \[{\text{1}}\].
So, the prime factorization of \[180\] is
\[180 = 2 \times 2 \times 3 \times 3 \times 5\]
        \[ = {2^2} \times {3^2} \times 5\]

Note: While solving questions similar to the one given above, remember that prime factorization is the method of factoring a number in terms of prime numbers, with prime numbers as the variables. The method of identifying prime numbers and multiplying them together to get the original number is known as prime factorization. The prime factors of \[{\text{16}}\] are, for example, \[2{\text{ 2 2 2}}\]. It's also possible to write this as \[{\text{24}}\]. The division method and the factor tree method are two methods for determining a number's prime factors.