Question

In which of the following expressions prime factorization has been done:
A. $ 24 = 2 \times 3 \times 4 $
B. $ 56 = 7 \times 2 \times 2 \times 2 $
C. $ 70 = 2 \times 5 \times 7 $
D. $ 54 = 2 \times 3 \times 9 $

Answer 1

Hint: Here we will first identify the prime numbers and then will observe the given multiple choices whether it is prime or composite numbers. Prime numbers have only two factors, the number itself and the number one whereas the composite numbers are the numbers which have more than two factors.

Complete step-by-step answer:
Prime factorization can be well-defined as the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are well-defined as the numbers which are greater than $ 1 $ and which are also not the product of any two smaller natural numbers.

A. $ 24 = 2 \times 3 \times 4 $
In the above expression, the number $ 4 $ is the composite number and not the prime number and the expression is not in the form of the product of the prime numbers.

B. $ 56 = 7 \times 2 \times 2 \times 2 $
In the above expression all the given terms are the product of the prime numbers.

C. $ 70 = 2 \times 5 \times 7 $
In the above expression all the given terms are the product of the prime numbers.

D. $ 54 = 2 \times 3 \times 9 $
In the above expression, the number $ 9 $ is the composite number and not the prime number and the expression is not in the form of the product of the prime numbers.

Here, we can observe that $ 2,3,5,7 $ are the prime numbers and $ 4,6,8,9 $ are the composite numbers.
Hence, option B and C are the expressions which are expressed as the product of the prime numbers.
So, the correct answer is “Option B and C”.

Note: Be good in finding the prime factorization for the given terms being good in multiples and division. Prime factorization can be calculated by using other methods like the factor tree method. Be clear with the difference between the prime numbers and the composite numbers. Composite numbers are expressed as the product of prime numbers which have more than two factors. To get the factors, be good in multiples and remember at least twenty.