Question

What is the prime factorization of 476?

Answer 1

Hint: First of all we need to understand the meaning of prime factorization of a number. Now, we will write the given composite number as the product of all of its prime factors to get the answer. Here, prime factors means those numbers which itself do not have more than two factors.

Complete step-by-step solution:
Here we have been provided with the number 476 and we are asked to determine its prime factorization. First let us understand the meaning of prime factorization.
Now, in mathematics the prime factorization of a number is a method by which we write that number as the product of all of its prime factors. The term prime numbers means those numbers which itself do not have more than two factors. For example: - if we have to write 20 as the product of its prime factors we can write it as $20=2\times 2\times 5$. Here, as you may see that all the numbers in the R.H.S are prime numbers.
Let us come to the question. Here we have the number 476 so using the prime factorization method we get,
\[\begin{align}
  & 2\left| \!{\underline {\,
  476 \,}} \right. \\
 & 2\left| \!{\underline {\,
  238 \,}} \right. \\
 & 2\left| \!{\underline {\,
  119 \,}} \right. \\
 & 7\left| \!{\underline {\,
  17 \,}} \right. \\
\end{align}\]
We can see that there are three different prime factors 2, 7 and 17, so we can write,
$\Rightarrow 476=2\times 2\times 2\times 7\times 17$
In exponential form we can write,
\[\therefore 476={{2}^{3}}\times 7\times 17\]

Note: Note that the prime factorization is very useful in calculating square roots of a number and to check if they are perfect squares or not. If all the factors can be written as the exponent of 2 then the number is a perfect square otherwise not. This method is also helpful while calculating the L.C.M and H.C.F of two or more numbers.