Question

How do you write the prime factorisation of 68?

Answer 1

Hint: In the given question we have to find the prime factorisation of the integer 68 .So the prime factorisation of an integer involves dividing the number with its factors which are prime and not the composite factors until there are no prime factors remaining and the given question integer is simplified. So, for 68 we will start with 2 as the prime factor and proceed until we get 1.

Complete step-by-step solution:
In the above given question it states that we have to find the prime factorisation of the composite number 68 which means we have to find the factors of number 68 which can’t further be divided or reduced into factors or simply we can say we have to find the factors of number 68 which are prime number ones. Since the given number 68 is even number we start the splitting as \[2\times ....\]
\[2\left| \!{\underline {\,
  68 \,}} \right. \]
\[2\left| \!{\underline {\,
  34 \,}} \right. \]
Here in this number 2 is a prime number whereas the number 34 is not a prime number so we further split the number 34 as follows
\[2\left| \!{\underline {\,
  68 \,}} \right. \]
\[2\left| \!{\underline {\,
  34 \,}} \right. \]
\[17\left| \!{\underline {\,
  17 \,}} \right. \]
\[1\left| \!{\underline {\,
  1 \,}} \right. \]
\[1\]
Here in this case we have 2 which is a prime number as well as 17 which is also a prime number. So the required solution of prime factorisation of the number 68 is as follows
\[\Rightarrow 68=2\times 2\times 17\]

Note: In the questions of these kind of factorisation we have to be careful in knowing the concept of prime numbers for example if we take in this case of factorisation of number 68 \[\Rightarrow 68=2\times 34\] if we conclude this as our solution it will be wrong because the number 34 is not a prime number so we have to be careful in doing those kind of questions. The solution must be a complete prime number factor \[\Rightarrow 68=2\times 2\times 17\] which is this in this case.