Question

What is \[52\] as a product of primes?

Answer 1

Hint: In order to find out \[52\] as a product of primes, firstly we have to find out the prime numbers that divide \[52\]by the method of prime factorization. After the prime factorization of \[52\], we get the prime numbers. The product of these prime numbers would be the required answer.

Complete step by step answer:
Now, let us know about the method of prime factorization. Prime factorization of any number means to represent that number as a product of prime numbers. A prime number is a number that has exactly two factors 1 and the number itself. This process has to be carried forward until the received quotient would be \[1\].
Now let us start finding out the prime factors of \[52\] by the method of prime factorization.
\[\begin{align}
  & 2\left| \!{\underline {\,
  52 \,}} \right. \\
 & 2\left| \!{\underline {\,
  26 \,}} \right. \\
 & 13\left| \!{\underline {\,
  13 \,}} \right. \\
\end{align}\]
    \[\left| \!{\underline {\,
  1 \,}} \right. \].
Now, \[52\] can be expressed in the form of a product of primes as shown below.
\[52=2\times 2\times 13\]
The common prime factors are \[2\] and \[13\].

Note: Prime factorization is useful in finding HCF and LCM of numbers. It is widely used in cryptography as the study of secret codes is known as cryptography. Prime numbers are used to form or decode those codes. There are two common ways to perform prime factorization. The first is called the Prime Factor Tree, and the second is known as the Upside-Down Division. The common prime factors can be expressed in the form of exponents too.