Question

How do you write the prime factorisation of $22$?

Answer 1

Hint: The prime factorisation of any number can be written by using the long division method. In this method, we divide the given number by the smallest prime number by which the number is divisible. The division by the prime number is done repeatedly until the quotient is not divisible by the prime number. Then we proceed to the next smallest prime number to divide the quotient, and so on until the quotient is obtained equal to one. For writing the prime factorisation of the given number $22$, we have to start by dividing it by the smallest prime number, which is equal to $2$. Then proceeding with the other prime numbers until the quotient becomes equal to one, we will obtain the required prime factorisation.

Complete step-by-step answer:
According to the question, we need to write the prime factorisation of the number $22$. Let us use the long division method for this. We start with choosing the smallest prime number, which is $2$, as the divisor, since the given number $22$ is divisible by $2$.
\[\begin{align}
  & 2\left| \!{\underline {\,
  22 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  11 \,}} \right. \\
\end{align}\]
The quotient is equal to $11$, which is itself a prime number. So the next prime divisor must be $11$ so that we complete the prime factorisation as
\[\begin{align}
  & 2\left| \!{\underline {\,
  22 \,}} \right. \\
 & \text{11}\left| \!{\underline {\,
  11 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}\]
Since we obtained the quotient equal to one, the prime factorization of the given number is completed as $2\times 11$.
Hence, we write the prime factorization of $22$ as $2\times 11$.

Note: We can also use the factor tree method to write the prime factorization of the given number. In this method, we write the given number as a multiplication of two numbers, in which one number is equal to a prime number. This process has to be repeated until the number is obtained as the multiplication of all the prime numbers.