Question

How $252$ can be expressed as a product of primes:
(A) $2 \times 2 \times 3 \times 3 \times 7$
(B) $2 \times 2 \times 2 \times 3 \times 7$
(C) $3 \times 3 \times 3 \times 3 \times 7$
(D) $2 \times 3 \times 3 \times 3 \times 7$

Answer 1

Hint: In this question we have to find the prime factorization of the given number. We know that the prime factorization of a number is splitting the given number into the set of prime numbers which can generate the original number by multiplying the set of prime numbers. So, in this question we will split the original number into the set of prime numbers.

Complete step by step solution: The original number given is $252$ . We have to find the prime factorization of the given number by breaking the number into its prime factor.
We can write $252$ as follows:
$ \Rightarrow 252 = 126 \times 2$
Now $126$ can be written as $63 \times 2$ . Therefore, the above equation becomes:
$ \Rightarrow 252 = 63 \times 2 \times 2$
Now $63$ can be written as $21 \times 3$ . Therefore, the above equation becomes:
$ \Rightarrow 252 = 21 \times 3 \times 2 \times 2$
Now $21$ can be written as $7 \times 3$ . Therefore, the above equation becomes:
$\Rightarrow 252 = 7 \times 3 \times 3 \times 2 \times 2$
$\Rightarrow 252 = 2 \times 2 \times 3 \times 3 \times 7$
Therefore, we have split the given number $252$ into the set of prime numbers and by multiplying this prime number we will get our original number.
Therefore, we can say that the prime factors of $252$ are $2 \times 2 \times 3 \times 3 \times 7$ .

Hence, the correct option is (A).

Note: In this question the important thing is the definition of prime factorization if we know the definition of prime factors then we can easily find out the prime factors of the given numbers. And the other important thing is the splitting of the given number into its prime factor. So, be careful about these things while solving the questions on the prime factorization.