Question

Which expression is the prime factorisation of 252?

F.$2^2\cdot 3^2\cdot 7^2$

G.$2^2\cdot 3^2\cdot 7$

H.$2\cdot 3^2\cdot 7$

I.$2\cdot 3^2\cdot 7^2$

Short answer

The correction is G which is $2^2\cdot 3^2\cdot 7$.

Step-by-step solution

Step 1  . Apply the concept of prime factorization 

In this, simply use the concept of prime factorization of the numbers by dividing the number by suitable digit of prime number to make the quotient small.

Step  2  . Find the Factorization 

Here, the numbers is 252.

Simply divide the above number by suitable digit until to get the smallest quotient,

$\begin{array}{l}252÷2=126\\ 126÷2=63\\ 63÷3=21\\ 21÷3=7\\ 7÷7=1\end{array}$

Here is the list of all Positive Factors of 252 in numerical order: $2,2,3,3,7.$

So, on combining it becomes $2^2\cdot 3^2\cdot 7$.

Step  3  .Eliminating the other options to get the correct one

F.$2^2\cdot 3^2\cdot 7^2$: It is the incorrect option because the correct factorisation is $2\times 2\times 3\times 3\times 7$.

G.$2^2\cdot 3^2\cdot 7$: It is the correct option because the correct factorisation is$2\times 2\times 3\times 3\times 7$.

H.$2\cdot 3^2\cdot 7$: It is the incorrect option because the correct factorisation is$2\times 2\times 3\times 3\times 7$.

I.$2\cdot 3^2\cdot 7^2$: It is the incorrect option because the correct factorisation is $2\times 2\times 3\times 3\times 7$.