Question

Which one of the following is a prime number?
A. 261
B. 221
C. 373
D. 437
E. None of these

Answer 1

Hint: First of all we have to know what a prime number is. Then we have to understand the process of factorization. And then we have to take each option in the question and make factors to know which one is a non-prime number. During this process we cannot find any factor other than 1 or the number itself. Then that will be the asked prime number in the question.

Complete step by step answer:
We know that in mathematics, prime numbers are whole numbers greater than 1, that have only two factors 1 and the number itself. Prime numbers are divisible only by the number 1 or itself. For example, 2, 3, 5, 7 and 11 are the first few prime numbers.
Now we have to take each option in the question and test whether it is a prime or not.
But firstly we have to know the term factorization. Factors of a number are numbers that divide evenly into another number. Factorization writes a number as the product of smaller numbers.
Firstly if we take 261 and start factorization we can see,
\[\begin{align}
  & \text{ }3\left| \!{\underline {\,
  261 \,}} \right. \\
 & \text{ }3\left| \!{\underline {\,
  87 \,}} \right. \\
 & 29\left| \!{\underline {\,
  29 \,}} \right. \\
 & \text{ }1 \\
\end{align}\]
After factorization we can write 261 as \[261=3\times 3\times 29\]. Clearly it is not a prime number.
Now for 221 we can see,
\[\begin{align}
  & 13\left| \!{\underline {\,
  221 \,}} \right. \\
 & 17\left| \!{\underline {\,
  17 \,}} \right. \\
 & \text{ }1 \\
\end{align}\]
After factorization we can write 221 as \[221=13\times 17\]. Clearly it is also not a prime number.
Now for 437 we can see,
\[\begin{align}
  & 19\left| \!{\underline {\,
  437 \,}} \right. \\
 & 23\left| \!{\underline {\,
  23 \,}} \right. \\
 & \text{ }1 \\
\end{align}\]
As we can see it is not a prime number either. It can be written as \[437=19\times 23\].
But for the number 437 we can see that the number is divisible only by the number 1 or itself which is 437.

So clearly we can conclude that the number 437 (Option D) is the prime number.

Note:
To solve this question students have to know the first few prime numbers like 2, 3, 5, 7, 11, 13 etc. and its multiples. Students also remember the process of factorization otherwise they cannot figure out the non-prime number present in the questions.