Question

Which of the following numbers are prime?
$
  {\text{(a) 23}} \\
  {\text{(b) 51}} \\
  {\text{(c) 37}} \\
  {\text{(d) 26}} \\
$

Answer 1

Hint: - Here, we factorize the numbers to see whether it is prime or not.

Complete step-by-step solution -

A prime number (or a prime) is a natural number greater than $1$ that is not a product of two smaller natural numbers A natural number greater than $1$ that is not prime is called a composite number For example, $5$ is prime because the only ways of writing{ it as a product ${\text{1}} \times {\text{5}}\ $ or ${\text{5}} \times {\text{1}} $ involve $5$itself.
${\text{(a) 23 = }}$ It is only written as ${\text{(1}} \times {\text{23)}}$ $\therefore $ it is a prime number
${\text{(b) 51 = }}$ It is only written as ${\text{(1}} \times {\text{3}} \times {\text{17)}}$ $\therefore $ it is not a prime number
${\text{(c) 37 = }}$ It is only written as $(1 \times 37)$ $\therefore $ it is a prime number
$({\text{d) 26 = }}$ It is only written as $(1 \times 2 \times 13)$$\therefore $ it is not a prime number

Note: - This is defination type question we need to remember the definition and The property of being prime is called primality. A simple but slow method of checking the primality of a given number $n$ called trial division, tests whether$n$ is a multiple of any integer between $2$ and$\sqrt {\text{n}} $