Question

Here are factor trees of the number $90$. Write the missing numbers:
 

Answer 1

Hint: The key to solve problems of this type is to have a good understanding of prime factorization. We need to perform factorization using the factor tree method which is a tool that breaks down any number into its prime factors. Here, if we perform prime factorization of the whole number $90$, we will get the required solution.

Complete step-by-step answer:
Here, we need to perform prime factorization of the whole number $90$.
According to the given information, we know that we will have to use the tree factor method for factoring $90$.
Firstly, we will divide $90$ by $2$, as $2$ is the first prime number.
$\Rightarrow {\displaystyle \frac{90}{2}}=45$
Now, we get $2$ as the prime factor of $90$.
Hence, $90$ can be written as the multiple of two numbers $2\times 45$.
We will draw the branches below,

Now, we have another number which is $45$. On dividing it by $2$we don’t get an integer solution.
Also we will leave $2$undisturbed as it is a prime number and one of the prime factors that we have obtained.
Further, we will represent$45$ as a product of two numbers, take it to be $9\times 5$.
We will draw the required branches below,

As we move forward, we will leave $5$undisturbed as it is a prime number and one of the prime factors that we have obtained.
So our focus shifts on the other number which is $9$. On splitting $9$into product of two numbers, we will get
$\Rightarrow 9=3\times 3$
We will draw the required branches below,

We can’t split it anymore as we have achieved the desired factor tree and on highlighting the prime factors we will complete the factor tree for the given number $90$.

Note: The key to solve problems of this type is to have a good understanding of prime factorization.
Here, if we perform prime factorization of the whole number $90$, we will get the required solution.
Also the multiplication of the last two will give the preceding number.