Question

Find the product of unit digit of product \[(256\times 27\times 159\times 182)\].

Answer 1

Hint: We should know that the unit digit of product of n numbers can be found by finding the unit digit of product of unit digit of each and every number of n numbers. Now we will write a unit digit of 256. In the similar manner, we will write a unit digit of 27. In the similar manner, we will write a unit digit of 159. In the similar manner, we will write a unit digit of 182. Now we will do the product of unit digits of 256, 27, 159 and 182. After obtaining the product we will find the unit value of the product. This will give the unit digit in the product \[(256\times 27\times 159\times 182)\].

Complete step-by-step answer:
Before solving the problem, we should know that the unit digit of product of n numbers can be found by finding the unit digit of product of unit digit of each and every number of n numbers.
In this problem, we should find the unit digit of the product of \[(256\times 27\times 159\times 182)\].
It is clear that the
Unit digit of 256 is equal to 6.
Unit digit of 27 is equal to 7.
Unit digit of 159 is equal to 9.
Unit digit of 182 is equal to 2.
We know that the unit digit of product of n numbers can be found by finding the unit digit of product of unit digit of each and every number of n numbers.
So, now we should find the product of 6, 7, 9 and 2.
\[\begin{align}
  & \Rightarrow \text{Product = 6}\times \text{7}\times \text{9}\times \text{2} \\
 & \Rightarrow \text{Product= 42}\times \text{9}\times \text{2} \\
 & \Rightarrow \text{Product = 378}\times \text{2} \\
 & \Rightarrow \text{Product =756} \\
\end{align}\]
Now we get the product of 6,7,9 and 2 as 756. The unit digit of 756 is 6.
So, the unit digit of product of 256, 27, 159, 182 is equal to 6.

Note: This sum can be solved in an alternative method.
In the question, we should find the unit digit of the product of \[(256\times 27\times 159\times 182)\].
By directly finding the product of \[(256\times 27\times 159\times 182)\], we can get the unit digit of the given product.
\[\begin{align}
  & \Rightarrow \text{Product =256}\times \text{27}\times \text{159}\times \text{182} \\
 & \Rightarrow \text{Product =6912}\times \text{159}\times \text{182} \\
 & \Rightarrow \text{Product =1099008}\times \text{182} \\
 & \Rightarrow \text{Product =200019456} \\
\end{align}\]
So, the product of \[(256\times 27\times 159\times 182)\] is equal to 200019456.
So, the unit digit of 200019456 is equal to 6.