Question

What is the prime factorization of \[44\] ?

Answer 1

Hint: The prime factorization of \[44\] is nothing but finding out the prime numbers that divide \[44\] exactly. After the method of prime factorization, we obtain a product of prime factors that would be equal to \[44\]. So firstly, we will be performing the prime factorization method upon \[44\], and then we get the required product.

Complete step by step solution:
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 performing our prime factorization.
\[\begin{align}
  & 2\left| \!{\underline {\,
  44 \,}} \right. \\
 & 2\left| \!{\underline {\,
  22 \,}} \right. \\
\end{align}\]
   \[\left| \!{\underline {\,
  \text{11} \,}} \right. \]
Now, we can express \[44\]as the product of primes as shown below.
\[\text{44=2}\times \text{2}\times \text{11}\]
\[\therefore \] The prime factorization of \[44\] is \[\text{44=2}\times \text{2}\times \text{11}\].
If the same prime factors repeat, we can express them in the form of exponents. In our case, \[2\] ahs repeated twice. So this can be expressed as shown below.
\[\text{44=}{{\text{2}}^{2}}\times \text{11}\]

Note: Prime factorization is useful in finding HCF and LCF 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.