Question

What is the prime factorization of $3528$ ?

Answer 1

Hint: First, we will need to know about the prime numbers and composite numbers.
Prime numbers are the numbers that are divisible by themselves and $1$ only or also known as the numbers whose factors are the given number itself.
But the composite numbers which are divisible by themselves, $1$ and also with some other numbers (at least one number other than $1$ and itself)
Every composite number can be represented in the form of prime factorization.

Complete step-by-step solution:
Since from the given that we asked to find the prime factorization of the number $3528$.
If the given number is prime then we cannot find its prime factorization. Now to check if the given number is prime or composite.
Since Prime numbers are the numbers that are divisible by themselves and $1$ only. But the number $3528$ can be divisible by $2,3,4,6,7,...$ and some other numbers and thus which is a composite number.
Since $3528$ is a composite that is divided by the number $7$ and now separates that into rewrite the number as to $3528 = 7 \times 504$ where $7$ is prime so don’t change that, again we get $3528 = 7 \times 7 \times 72$. Now since $72$ is composite which is divided by the number $3$ (twice) . Hence rewrite it as $3528 = {7^2} \times {3^2} \times 8$ where $3$ is prime so don’t change that. Now since $8$ is composite which is divided by the number $2$ (three times). Hence rewrite it as $3528 = {7^2} \times {3^2} \times {2^3}$ where $2,3,7$ are prime.
This process can be expressed as in the form of table too,
$
  7\left| \!{\underline {\,
  {3528} \,}} \right. \\
  7\left| \!{\underline {\,
  {504} \,}} \right. \\
  3\left| \!{\underline {\,
  {72} \,}} \right. \\
  3\left| \!{\underline {\,
  {24} \,}} \right. \\
  2\left| \!{\underline {\,
  8 \,}} \right. \\
  2\left| \!{\underline {\,
  4 \,}} \right. \\
  2\left| \!{\underline {\,
  2 \,}} \right. \\
  1\left| \!{\underline {\,
  1 \,}} \right. \\
 $
Therefore, the prime factorization process is done because all the numbers can be rewritten as in the form of prime and the hence prime factorization of the number $3528$ is ${7^2} \times {3^2} \times {2^3}$.

Note: Since don’t write the number ${3^2} = 9$ because $9$ is the composite number, and thus ${3^2}$ is the repeated prime number while in the process of prime factorization.
We can find whether the given number is prime or composite by the trial-and-error methods. Divide the number with the prime numbers less than the given number. if the number is exactly divisible by the prime number, it is the composite number, if not then it is the prime number.
The only even prime number is $2$ and all other prime numbers are odd.