Question

Write the prime factorization of 85.

Answer 1

Hint:Prime factorization is the process of finding the prime terms or prime factors which when multiplied gives the original number. So for performing prime factorization we divide the original number with prime numbers which are divisible with it and then stop the process only when the end result is a prime number.
Here the number on which prime factorization is to be performed is 85. So first we have to find the prime numbers that are fully divisible with 85 giving quotients that is a whole number rather than a mixed fraction. Then we have to represent those prime numbers in the form of a factor tree.

Complete step by step solution:
Given
\[85 \ldots \ldots ..\left( i \right)\]Number on which prime factorization is to be performed.
Considering the prime numbers for the division process we know that 85 is divisible by 5:
$ \Rightarrow \dfrac{{85}}{5} = 17$
Since 17 is a whole number and a prime number the next step would be as follows.
$ \Rightarrow \dfrac{{17}}{{17}} = 1$
Therefore the answer would be: $85 = 5 \times 17$ since both 5 and 17 are prime numbers.
So the prime factorization of 85 can be written as $85 = 5 \times 17$.
Additional Information:
Factor Tree:
We know that 85 is a composite number so we can draw its factor tree from its factors as shown below:
$
\;\;\,\;\;85 \\
\;\; \swarrow \;\;\; \searrow \\
5\;\;\;\;\;\;\;\;\;\;17 \\
\;\;\;\;\;\;\;\;\; \swarrow \;\,\, \searrow \\
\;\;\;\;\;\;\;\;17\;\;\;\;\;\;1 \\
$
Factor tree is helpful in showing any factors of a number till the last step of factorization.

Note: A prime number can be divided only by 1 or itself such that it cannot be factored further. A composite number is a number which can be divided by one, itself and any other natural number. Also every other whole number can be broken down into prime number factors such that prime numbers form the basic building blocks of all numbers.