Question

Which one of the following is a prime number?
$
  {\text{A}}{\text{. 119}} \\
  {\text{B}}{\text{. 187}} \\
  {\text{C}}{\text{. 247}} \\
  {\text{D}}{\text{. 551}} \\
  {\text{E}}{\text{. None of these}} \\
$

Answer 1

Hint – To find the prime number, we write all the factors of each of the numbers given in the options, if a number has only 1 and itself as factors, then it is prime.

Complete step-by-step answer:

Given data, prime number.
Prime numbers have only two factors, one and itself.
For example, 2, 3, 5, 7, 11, 13, 17, 19 ……..

Now let us factorize each of the options:
119
It can be expressed as 1 × 119 and 7 × 17.
Hence 119 is not a prime number.

187
It can be expressed as 1 × 187 and 11 × 17.
Hence 187 is not a prime number.

247
It can be expressed as 1 × 247 and 13 × 19.
Hence 247 is not a prime number.

551
It can be expressed as 1 × 551 and 19 × 29.
Hence 551 is not a prime number.

Hence none of the above numbers is prime, none of the options is prime. Hence Option E is the correct answer.

Note – In order to solve this type of question the key is to know the definition of a prime number. Here we directly expressed the number in terms of its factors. For slightly complex numbers we find the prime factors using the prime factorization method or by using a factor tree method.