Question

What is the prime factorization of \[23\]?

Answer 1

Hint: We use the concepts of prime numbers and definitions of prime numbers to solve this problem. And we will see some examples of prime factorizations of few numbers and hence, find the solution for this problem. Prime numbers are the numbers which have only two factors i.e., 1 and the number itself.

Complete answer:
A prime number is a natural number greater than 1, which is divisible only by 1 and the number itself.
So, in other words, numbers which have only two divisors have been called prime numbers.
All other numbers other than prime numbers are called composite numbers.
For example, take the natural number 2.
So, the number 2 is only divisible by two numbers which are 1 and 2. So, 2 is a prime number.
Take another example 5, which is also having two divisors 1 and 5. So, 5 is also a prime number.
These are the few prime numbers:
\[2,3,5,7,11,13,17,19,23,29,31,......\]
Every composite number can be written as a product of prime numbers.
For example, take number 24, which is a composite number.
So, we can write 24 as, \[24 = 2 \times 2 \times 2 \times 3\]
This is called prime factorization.
And suppose that \[p\] is a prime number, then it can be written as \[p \times 1\].
Now in the question, the number 23 is given.
This number is only divisible by 1 and 23 only.
So, 23 is a prime number.
Hence, it can be written as \[23 = 23 \times 1\]
So, this is the prime factorization of the number 23.

Note:
The number 1 is neither a prime number nor a composite number. And the number 2 is the least prime number. Every composite number can be written as a product of prime numbers.
And, prime factorization of every prime number is 1 multiplied by itself only.