Question

How do you write the prime factorization of $280?$

Answer 1

Hint: It is also called integer factorization. It is the process of breaking a number down into the set of prime numbers which multiply together to result in the original number. We have to use only prime numbers. Prime numbers are those numbers whose factors are 1 and itself. For example, we have 2. $2$ can only be written as $2=2\times 1$ . It can’t be written in any other form. So the factors of $2$ are $2$ and itself. Hence $2$ is a prime number. And other numbers existing this way are also prime numbers.

Complete step by step answer:
So now let’s see how we can expand $280.$
$5$ is a factor of $280$ . So let’s start with that.
$\Rightarrow 280=5\times 56$ .
$7$ is a factor of $280$ . So now let’s expand $56$ using $7$. Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 280=5\times 56 \\
 & \Rightarrow 280=5\times 7\times 8 \\
\end{align}$
As we see $8$ .$2$ is a factor of $8$. Let’s expand $8$ using $2$ . Upon doing so, we get the following :
$\begin{align}
  & \Rightarrow 280=5\times 7\times 8 \\
 & \Rightarrow 280=5\times 7\times 2\times 2\times 2 \\
 & \Rightarrow 280=5\times 7\times {{2}^{3}} \\
\end{align}$ .
As we can see all the numbers we used here are prime numbers. We didn’t use any composite numbers. Composite numbers are the opposite of prime numbers. Composite numbers have factors other than $1$ and itself. Example : 10, 15, 16 etc.

$\therefore $ Hence , as we can see, the prime factorization of $280=5\times 7\times {{2}^{3}}$ where we used only prime numbers.

Note: Be careful while expanding the numbers . And we always have to make sure that we expand the given number using only prime numbers. And just for the sake of simplicity always start with the smallest prime number to expand. So that there would be no confusion and smooth completion of the answer.