Question

How can we write \[13\] as a product of prime numbers?

Answer 1

Hint: A prime number is a number which has only two factors i.e. \[1\] and the number itself. Now, we have to express \[13\] as a product of prime numbers, which means that we have to write \[13\] as a product of numbers which are prime. For example, If we have to express \[a\] as a product of prime numbers, we must have prime numbers \[b,c,d,.....,n\] such that \[a = b \times c \times d \times ...... \times n\]. So, let us see whether we can write \[13\] as a product of prime numbers or not.

Complete step-by-step answer:
We need to write \[13\] as a product of prime numbers.
Let us first prime factorise \[13\].
We see that there are no factors of \[13\] other than \[1\] and \[13\].
By definition of prime numbers, we can say that \[13\] is a prime number.
Hence, \[13\] can be written as
\[ \Rightarrow 13 = 1 \times 13\]
We cannot write \[13\] in any other way.
Here, we see that \[13\] can be written as a product of \[1\] and \[13\].
Now, let's see whether these two numbers are prime or not.
Above, we saw that \[13\] is a prime number but we know that \[1\] is neither prime nor composite. Hence, we cannot say that \[1\] is a prime number. Hence, \[13\] cannot be written as a product of primes but \[13\] can be written as \[13\] only.
So, the correct answer is “[13\]”.

Note: We must note that a prime number cannot be written as a product of prime numbers but only a composite number can be written as a product of prime numbers. Also, we must remember that \[1\] is neither prime number nor composite number (A number which has more than two factors). If we consider \[1\] as a prime number then we will come to a conclusion that a prime number can be written as a product of prime numbers.