Question

Express each of the following as product of powers of prime factors.
1) 5,324​

Answer 1

$\large\underline{\sf{Solution-}}$

Basic Concept :-

• Prime Factorization" is finding which prime numbers multiply together to make the original number.

How to find prime factorization :-

• Step 1: Start by dividing the number by the first prime number 2 and continue dividing by 2 until you get a decimal or remainder. Then divide by 3, 5, 7, etc. until the only numbers left are prime numbers.

• Step 2: Write the number as a product of prime numbers.

Let's solve the problem now!!

$\rm :\longmapsto\:Prime \: factorization \: of \: 5324$

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:5324\:\:\:}}}\\ {\underline{\sf{2}}}& \underline{\sf{\:\:2662\:\:\:}} \\\underline{\sf{11}}&\underline{\sf{\:\:1331\: \:\:}}\\{\underline{\sf{11}}}&{\underline{\sf{\:\:121\:\:\:}}} \\{\underline{\sf{11}}}&{\underline{\sf{\:\:11\:\:\:}}} \\ {\underline{\sf{}}}&{{\sf{\:\:1\:\:\:}}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

$\rm :\implies\:Prime \: factorization \: of \: 5324 = {2}^{2} \times {11}^{3}$