Question

How do you write the prime factorization of $87$ ?

Answer 1

Hint: In this question, we have to find the prime factorization of a number. As we know, prime factorization means finding prime numbers and then multiplies those numbers to get the original number. Prime numbers are those numbers that are divisible to $1$ or itself. Thus, in this problem, we start solving by finding the prime factors of the number $87$. First, we take the number $2$, but we see that $2$ is not a factor of $87$, therefore we go to the next number that is $3$ . Now, we see that $3$ is a prime number and when we divide $87$by $3$, we get the remainder 0 , therefore we get that $3$ is one of the prime factors of $87$. Therefore, we then go to the next number and solve it until we get the required solution to the problem.

Complete step by step answer:
According to the question, we have to find the prime factorization of a number.
The number given to us is $87$ .
Thus, we start solving this problem by finding the prime factors of the number.
Now, we know $1$ is neither a prime number nor composite number, thus we take the next number that is $2$ .
Since $2$ is the prime number, but we see that it is not a factor of $87$. Therefore, we take the next number $3$ .
Thus, we see that $3$ is a prime number and when we divide $87$ by $3$ , we get the remainder as $0$
$\begin{align}
  & \Rightarrow 87\div 3=29\text{ - quotient} \\
 & \Rightarrow \text{87}\div \text{3=0 - remainder} \\
\end{align}$
Now, we take the next number $4$, since this number is not a prime number therefore we go to the next number.
Therefore, we take the next number $5$ , we see that this number is a prime number, therefore, we now calculate whether it is divisible by 87 or not, that is
$\begin{align}
  & \Rightarrow 87\div 5=17.4\text{ - quotient} \\
 & \Rightarrow 87\div 5=2\text{ - remainder} \\
\end{align}$
Thus, we see above that we did not get the remainder 0, therefore $5$ is not the prime factor of $87$. Therefore, we take the next number $6$ .
We see that $6$ is not a prime number, thus we go to the next number $7$ .
Now, $7$ is a prime number but when we divide $87$ by $7$ , it does not give the remainder as $0$ , thus $7$ is not a prime factor of $87$ .
As we know that the square of $7$ is greater than $29$ , thus no other factors are possible, that is
$\Rightarrow {{(7)}^{2}}=49>29$
Therefore, the prime factorizations of $87$ are $3$ and $29$ .

Note:
While solving this problem, keep in mind that 1 is neither a prime number nor a composite number, thus it is not a prime factorization of the number $87$. Also, after the number $7$, do not solve for all next numbers because it will take a lot of time.