Question

What is the prime factorization of 30?

Answer 1

Hint: For solving this question you should know about the prime factorization method. Prime factorization method used to calculate the prime factors of numbers. The prime factors are the factors of any number which are not divisible without self and one. So, these are known as prime factors because these are the prime values.

Complete step by step solution:
According to our question it is asked to find the prime factorization of 30.
So, the factors of a number are defined as the numbers which when multiplied to them they provide the original number again. By multiplying any two factors we get the original number.
Now, the factors of 30 are all the integers that can evenly divide the given number 30. If we find all possible factors of 30.
So, the factors of 30 are all the positive and negative integers which divide the number 30 completely. So, let us divide 30 by every number which completely divides it.
\[\begin{align}
  & 30/1=30,30/2=15, \\
 & 30/3=10,30/5=6, \\
 & 30/6=5,30/10=3, \\
 & 30/15=2,30/30=1 \\
\end{align}\]
So, the factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
But these are not prime factors.
Prime factorization of 30: To calculate prime factorization of 30, first we will take the least prime number that is 2. Divide it by 2 until it is completely divisible by 2. It is at a point that is not completely divisible then again takes the next prime number that is 3. Perform the same steps and move forward until we do not get 1, as the quotient.
Now, Step 1: Divide 30 with 2
                        \[30\div 2=15\]
Step 2: 15 is no more divisible by 2, move the next prime number that is 3
             \[15\div 3=5\]
Step 3: Now 5 is no more divisible by 3, move to the next prime number that is 5.
             \[5\div 5=1\]
Step 4: At the last divide 1 with 1 to get 1.
             \[1\div 1=1\]

So, the prime factorization of 30 is \[2\times 3\times 5\].

Note:
While solving this question you should be careful for the prime factorization of any number because we have to take only the prime numbers to get prime factors. If we take any even or odd number which is not prime then the question ad factors will be wrong completely.