Question

Prime factorization of \[25115\] has \[45\].

Answer 1

Hint: In order to check if \[25115\] has \[45\], firstly we must note down the prime factors of \[25115\]. After listing them, we must be checking for \[45\]. If the list possesses \[45\] as one of its factors then we can say that \[25115\] has \[45\].

Complete step-by-step solution:
Let us have brief information regarding prime factorization. Prime factorization is performed upon composite numbers to find the prime factors of the certain composite number. There are two common methods of performing prime factorization. They are the factor tree method and upside down division. The use of this method is to break down the number into primes in order to express them as a product of primes. If there occurs a single prime factor of a number multiple number of times, then can be expressed in exponential form.
Now let us perform the method of prime factorization on \[25115\] and check for \[45\].
We get,
\[\text{5}\left| \!{\underline {\,
  \text{25115} \,}} \right. \]
  \[\left| \!{\underline {\,
  \text{5023} \,}} \right. \]
So we obtain \[25115=5\times 5023\]
The prime factor of \[25115\] is \[5,5023\].
We can observe that there is no \[45\] in the list of prime factors of \[25115\].
\[\therefore \] Prime factorization of \[25115\] does not has \[45\]
Hence, the given statement is false.

Note: While solving this, we must have a note that \[45\] can only be a factor because it is not a prime number. We must remember that \[45\] will never be a prime factor to any number. We can perform prime factorization on a prime number but we must be acknowledging that the prime factor of the prime number will be the number itself.