Question

Find the prime factors of 156, and state the highest power of 2 in it.

Answer 1

Hint- Use the prime factorization method to break the number into the product of prime numbers. In prime factorization, if the same prime numbers happen to occur more than once, then these numbers are written in exponential form. Prime numbers are generally referred to as the number which can only be divided by the integer 1 and by itself. In other words, the numbers which are greater than 1 but are not the product of smaller numbers. When we factorize a prime number, then they will only have two factors 1 and the number itself.


Complete step by step solution:
To find the prime factors factorize the number 156, divide the number by the prime factors:
\[
   13\underline {\left| {156} \right.} \\
   2\underline {\left| {12} \right.} \\
   2\underline {\left| 6 \right.} \\
   3 \\
 \]
Hence the prime factors for the number 156 are:
\[\left( {156} \right) = 13 \times 2 \times 2 \times 3\]
We can see 2 occurs two times in the factorization hence, 2 is written in exponential form as:
\[\left( {156} \right) = 13 \times \underline {2 \times 2} \times 3 = 13 \times {\left( 2 \right)^2} \times 3\]
Here 2 is written in exponential form with power of 2.
Hence the highest power of 2 is 2
\[2 \times 2 = {\left( 2 \right)^2}\]


Note: Determining the factors through the prime factorization method is very essential as if the factors are not the prime number then, it may be possible that the answer will be wrong. Alternatively, this question can be solved by a long division method as well if the candidate is not comfortable with the above used table. But, it should be made clear that the long division method is quite time taking.