Question

What is the number of prime factors of $30030$ ?
A. Four
B. Five
C. Six
D. None of the above

Answer 1

Hint: Here we have to find the prime factors of the given numbers. So we will use the Repeated Division method for finding the prime factors of the number. Firstly we will take the least prime number and divide the number given by it until it is completely divisible by it. Then take the next prime number and repeat the same till we get our quotient as $1$. Finally calculate all the prime numbers used in the process and get the desired answer.

Complete step-by-step solution:
We have to find the prime factors of the below number:
$30030$
We will use the Repeated Division method for finding the prime factors of $30030$.
Firstly we will take the lowest prime number which is $2$ and divide the number $30030$ by it until it is completely divisible by it then we will take the next prime number which is \[3\] and keep on going like this until we get the quotient as $1$.
So we will find the prime factors of the number by Repeated Division method as follows:
$\begin{align}
  & 2\left| \!{\underline {\,
  30030 \,}} \right. \\
 & 3\left| \!{\underline {\,
  15015 \,}} \right. \\
 & 5\left| \!{\underline {\,
  5005 \,}} \right. \\
 & 7\left| \!{\underline {\,
  1001 \,}} \right. \\
 & 11\left| \!{\underline {\,
  143 \,}} \right. \\
 & 13\left| \!{\underline {\,
  13 \,}} \right. \\
 & \,\,\,\,\,\,\,1 \\
\end{align}$
So we can write the number $30030$ as follows:
$30030=2\times 3\times 5\times 7\times 11\times 13$
We get that there are six prime factors of the number $30030$
Hence the correct option is (C).

Note: Factors of the numbers divide the number completely with no remainder. Prime factors of the numbers are the prime numbers which divide the number completely. By multiplying all the factors of any number we get the number back. There are two ways to find the prime factor of a number which are The Repeated Division Method and Factor Tree Method.