Question

How do you create a factor tree for $204$ ?

Answer 1

Hint: For creating a factor tree for a given number $204$ , we will have to factorize the given number $204$into prime number. We will start from the number and after that we will write the two factors of the number that will give the original number with the production of that two numbers until we get the prime numbers of the number $204$.

Complete step by step answer:
Since, we have the number $204$ as a question. Now, we can write the number $204$ to the multiplication of the two numbers that are $4$ and $51$ as:
$\Rightarrow 204=4\times 51$
Now, for creating the factor tree, we will have to write it as:

Here, we can further factorize these two numbers as:
$\Rightarrow 4=2\times 2$
And
$\Rightarrow 51=3\times 17$
Now, we will write it in already created factor tree so that we can make progress in creating the factor tree as:

Since, the above factors $2$, $2$ , $3$ and $17$ are prime numbers that means we can not factorize these numbers further. So, the above diagram created with the factorization of numbers shows the factor tree.
Hence, the factorization of the number $204$ is $2$, $2$ , $3$ and $17$ that can be written as:
$\Rightarrow 204=2\times 2\times 3\times 17$

Note:
Since, we get the factor tree by factorization. Now, we can create a reverse tree by going downwards to upwards as:

Now, we can check it if it is correct or not by multiplication of these factorization as:
$\Rightarrow 2\times 2=4$
And
$\Rightarrow 3\times 17=51$
Now, we have two numbers that are $4$ and $17$ . Now, further we can multiply them for getting the given number $204$ as:
$\Rightarrow 4\times 51=204$
Hence, the solution is correct.