Question

Which of the following numbers are prime?
(i) 101
(ii) 251

Answer 1

Hint: Take each number and try to split it into a multiple of prime numbers or whole numbers. If it splits up then it is not a prime number. If it doesn’t have any factors except for 1 and the number itself, then it is a prime number.

Complete step-by-step answer:
A prime number is a natural number greater than 1 that is not a product of 2 smaller numbers. A natural number greater than 1 that is not prime is called a composite number. A prime number has only 1 and the number itself as factors.

We have been asked to find if 101 and 251 are prime numbers.

Both 101 and 251 are not divisible by any number or other prime numbers, 2, 3, 5, 7 etc.

The only factors of 101 are 1 and 101 and for 251 the only factors are 1 and 251.

\[\begin{align}
  & 101=1\times 101 \\
 & 251=1\times 251 \\
\end{align}\]

We cannot make any other numbers multiply together to make it.

Thus 101 is a prime number.

Similarly, 251 is also a prime number.


Note: We know that 1 is neither a prime number nor a composite number. All the prime numbers are odd, except for 2, which is the only even prime number.