Question

What is the prime factorization of 50?

Answer 1

Hint: We know that a prime number is a number greater than 1 which is not divisible by any value except 1 and the number itself. We can define factors as those numbers which when multiplied give another number. We have to find the prime factorization of 50. So, prime factorization is the method to find the prime factors of a number which when multiplied together gives the required number.
For example:
$\begin{align}
 & 20=2\times 2\times 5 \\
 & \\
\end{align}$
There are two methods to find the prime factors of a given number. One method is to find the smallest prime numbers that divide the given number completely and then continue the process further. Another method is to break the number into a combination of any factors as possible and then further break them down until you obtain prime factors of that number. This method is called the factor tree method.
Using this concept, we will find prime factorization of 50 by dividing 50 by 2 and continuing further.

Complete step by step solution:
Here, we need to find the prime factorization of 50. So, we’ll start dividing this number with the smallest possible prime number.i.e., 2.
$50\div 2=25$
Since 2 divides the number completely, so 2 is one of the prime factors of 50. Now, let's take the obtained number 25 and divide it by 2.
$25\div 2=12.5$
Since, 2 doesn’t divide 25 completely, so 2 is not the prime factor of 25. We can see a similar case with 3. So, let’s divide the number by 5,
$25\div 5=5$
So, 5 is also a prime factor of 50 as it completely divides 25. Now, the number that remains on dividing 25 by 5 is 5. Since 5 is itself a prime number, it can not be divided further by any number.so, this 5 is also a prime factor of 50.
So, the prime factors of 50 are:
$\begin{align}
 & 50=2\times 5\times 5 \\
 & \therefore 50=2\times {{5}^{2}} \\
\end{align}$
Hence, the prime factorisation of 50 is given by $50=2\times {{5}^{2}}$ .

Note: Another method to solve this question is via factor tree. Let us consider the number 50 as given in the question.
We can write 50 as the product of 25 and 2.
$50=25\times 2$
Now, 25 can further be broken as a product of 5 and 5.
$25=5\times 5$
Now, 5 cannot be further broken down into further prime factors as 5 is itself a prime number.
So, the prime factorization of 50 would be as follows:
$50=2\times 5\times 5$