Aptitude - Numbers - Discussion

To find unit digit in a large powered number, simply consider its last digit only. for suppose in (6374)^1793 take 4^1793 only. now note that any odd power of 4 gives a number with its unit digit as 4.so unit digit in (6374)^1793 is '4'.and then any power of 5 gives a number with 5 as its unit digit.so u.d in (625)^317 is '5'.then any power of 1 gives only 1 itself. so u.d in 341^491 is '1'. finally multiply all numbers i.e., 4*5*1 which gives 20 with u.d as 0.hence that result.

As in 6374 = unit digit is '4'
in 625 = unit digit is '5'
in 341 = unit digit is '1'.

Now just multiply all the digit units =4 * 5 * 1=20
In 20, the unit digit is '0'.

Again,
In the power of 6374 i.e,1793 = unit digit is '3',
In the power of 625 i.e, 317 = unit digit is '7',
In the power of 341 i.e, 491 = unit digit is '1',
Now multiply all the digit units = 3*7*1=21.
In 21, the unit digit is '1'.
Hence,
The required unit digit is, 0^1.
= 0 (answer).

Given question is.

{(6374)^1793 x (625)^317 x (341)^491}.

Ans:

NOTE: Unit digit for (4)^odd num is 4.

Unit digit for (4)^even num is 6.
Unit digit for (5)^any num is 5.
Unit digit for (1)^any num is 1.

Now apply the above conditions,

Unit digit of 6374 is 4.
Unit digit of 625 is 5.
Unit digit of 341 is 1.

Just multiply 4*5*1 = 20.

So unit digit of 20 is 0.

Answer is 0.

This can be done by this method too.

Just see the last number of the given number and the last number in the raise to find out the root.

Do the same for another two number.
Then you'll get three numbers after finding the root.
Then take the last numbers of these values and multiply them.

I checked it out for more other three example taken by myself and got it correct.

For a number ending in 4 ( like 6534) any odd power will have unit digit 4 and Even power unit digit 6 ( 1731 is odd and hence 6534 6 1731 will have unit digit 4.

For a number ending in 5 ( like 625 ) any odd or even power , unit digit will result in 5

For a number ending in 1 ( like 341 ) any odd or even power , unit digit will result in 1

4*5*1 = 20 - Unit digit 0.

4^2 = 16, 4^3 = 64. Unit digit = 4, when power is 3 (odd).

Unit digit of any number having odd power remains same as the original number has;here 6374^1793. Power is odd so unit digit will be 4, similarly 625^317 & 341^491 unit digits are 5 and 1 respectively, since power is odd.

So the unit digit of overall expression = (4.5.1) = 20 i.e. 0.

To find the unit digit of a number, you only need to consider the unit digits of the individual components and perform the operations.
Since the unit digit of 6374 is 4, 625 is 5, and 341 is 1, the unit digit of the entire expression will be (4^1793 * 5^317 * 1^491), which simplifies to 4 * 5 * 1 = 20.
The unit digit of 20 is 0.

7*7^107.
i.e 7^108.

We know 7^1 unit place will be 7.

7^2 unit place will be 9.
7^3 unit place will be 3.
7^4 unit place will be 1.

So unit place will be 7, 9, 3, 1 after these 7, 9, 3, 1 again and again.

We have 108 that is divisible by 4 so unit place will be one. You can find it on scientific calculator as well.

On the basis of cyclicity rule we easily find the unit digit .

4*5*1 = 0.
4^1 =4 5^1 =5 1^1=1.
4^2 =6 5^2 =5 1 cyclicity is 1.
4^3 =4 5 cyclicity is 5.
Cyclicity of 4 is 2.

Then 4^1793 divide 1793/3 = 1 4^1 = 4 as on...

Finally 4*5*1 = 0.

Consider this:

For,x=Odd, the unit place for 4^x is 4. The unit place for 5^x is 5, The unit place for 1^x is 1.
and x=Even, the unit place for 4^x is 6. The unit place for 5^x is 0, The unit place for 1^x is 1.

=>unit place means the digit present at the one's place(rightmost digit) of a number.