Question

Express the following numbers as a product of powers of prime factors:
(i) 72 (ii) 432

Answer 1

Solution :-

Express the Following Numbers as a Product of Power of Prime Factors :

i. 72

$\begin {gathered} \end {gathered}$

$\Large{ \begin{array}{c|c} \tt 2 & \sf{72} \\ \cline{1-2} \tt 2 & \sf {36} \\ \cline{1-2} \tt 2 & \sf{18} \\ \cline{1-2} \tt 3 & \sf{9} \\ \cline{1-2} \tt 3 & \sf{3}\\ \cline{1-2} \tt & \sf{1}\end{array}}$

Prime Factorization of 72 = $\bf 2 \times 2 \times 2 \times 3 \times 3$ = $\underline {\underline {\bf 2^3 \times 3^2}}$

$\begin {gathered} \end {gathered}$

ii. 432

$\begin {gathered} \end {gathered}$

$\Large{ \begin{array}{c|c} \tt 2 & \tt {432} \\ \cline{1-2} \tt 2 & \tt {216} \\ \cline{1-2} \tt 2 & \tt {108} \\ \cline{1-2} \tt 2 & \tt {54} \\ \cline{1-2} \tt 3 & \tt{27}\\ \cline{1-2} \tt 3 & \tt {9}\\\cline{1 - 2} \tt 3 & \tt 3\\\cline {1 - 2} \tt & \tt 1 \end{array}}$

Prime Factorization of 432 = $\bf 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3$ = $\underline {\underline {\bf 2^4 \times 3^3}}$

$\begin {gathered} \end {gathered}$

Additional Information :-

Prime Factorization :-

• Prime factorization is a Method in which we can Divide the numbers into the product of many numbers. The Numbers which obtains when doing this together when Multiplied results the number which we are solving. This should always done by prime numbers . . .

• This Prime Factorization is although the same as we calculate the LCM, Least Common Multiple, In Prime Factorization, we solve only with a single number, whereas in LCM we do with 2 or more numbers . . .

$\begin {gathered} \end {gathered}$

There are two Methods of Prime Factorization. They are -

• Factor Tree Method

• Division Method

$\begin {gathered} \end {gathered}$

Factor Tree Method :- We Factorise a Composite Number till we get all Prime Factors . . .

$\begin {gathered} \end {gathered}$

Division Method :- We Start Dividing the Given Number by the Smallest Prime Number and Continue Division by Prime Numbers till we Reach 1 . . .