Question

How do you write 42 as a product of its prime factors?

Answer 1

Hint: Here, we will use the prime factorization method to find the prime factors of the given number 42. Then we will multiply all the factors to express the given number as a product of its prime factors.

Complete step-by-step answer:
In this question, we are required to express the given number as a product of its prime factors.
We know that prime factors are those factors which are greater than 1 and have only two factors, i.e. factor 1 and the prime number itself.
Now, in order to express the given number as a product of its prime factors, we are required to do the prime factorization of the given number.
Now, factorization is a method of writing an original number as the product of its various factors.
Hence, prime factorization is a method in which we write the original number as the product of various prime numbers.
We will now factorize 42.
We can see that 42 is an even number, so dividing it by least prime number 2, we get
\[42 \div 2 = 21\]
Now dividing 21 by the next least prime number 3, we get
\[21 \div 3 = 7\]
Hence, 42 can be written as:
\[42 = 2 \times 3 \times 7\]
Hence, we have expressed the given number as a product of its prime factors.

Therefore, the required answer is:
\[42 = 2 \times 3 \times 7\]

Note: Here the given number is a composite number. A number is said to be a composite number if it is completely divisible by 2. We can express any composite number as a product number of prime factors. The smallest prime number is 2 and there are 25 prime numbers between 1 to 100. 1 is neither prime nor composite so it cannot be expressed as a product of prime factors.