Question

What are the factors of \[23\]? Is \[23\] prime or composite?

Answer 1

Hint: In this question we have to find the factors of \[23\]. Factors of a number are the whole numbers which when divided by that number gives remainder \[0\], that is the number is completely divisible by it’s factor. Here we will find the factors of \[23\] by the use of the factorization method.

Complete step-by-step answer:
Now, here we will use the factorization method to find the factors of the number\[23\].
In the factorization method, first of all consider the numbers \[1\] and \[23\] as factors of \[23\] and continue with finding the other pair of multiples of \[23\], which gives the results as an original number.
First we write the number \[23\].Then we will find the two numbers, which when multiplied to each other results in \[23\] , say \[1\] and \[23\], such that \[1{\text{ }} \times \;23 = 23\]. When we try other numbers which are between \[1\] and \[23\] we see that we cannot find any factor other than \[1\] and \[23\] . We see that \[23\] is perfectly divisible only by \[1\] and \[23\].
Hence, the factors of \[23\] are \[1\] and \[23\].
Since factors are \[1\] and the number itself it is a prime number.

Note: Prime numbers are those numbers, which can only be divisible by one and the number itself. Had there been any other perfect divisor of \[23\], we would have called it a composite number. A composite number is a number which can be written as a product of two integers, provided they are smaller than the number itself.