Aptitude - Numbers - Discussion

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.

Look here unit digit means the last digit.

Here we have - 6374*625*341=?
So, just see the last digit i.e 4,5,1 hence multiply them 4*5*1=20 now see the last digit i.e 0.

Therefore the answer is 0.

Thanks for explaining @Seema.

Actually, in case of 4^n.
if n=odd then unit digit is 4.
If n=even then the unit digit is 6.

This alternative pattern is true for all integers after 5. Digits before 5 also have a pattern put each integer has a different pattern.

A simple way to find unit digit.

6374 last number is 4.
625 last number is 5.
341 last number is 1.
So 4*5*1= 20.
20 last number is 0.
Hence the answer is 0.

So here is the concept;

Cyclicity rule Table for numbers.

1 -1
2 - 4 (2^1 =2 ,2^2=4 ,2^3=8, 2^4=6) 2^5=2 ,2^6=4 .
Again the numbers repeat there are 4 distinct values.

2, 4, 6, 8 so (2 - 4) now the same goes for all other numbers.

3 - 4 (3^1=3, 3^2=9, 3^3=7, 3^4=1),
4 - 2 (4^1=4, 4^2=6 ,4^3=4, 4^4=6),
5 - 1 (5^1=5, 5^2=5, 5^3=5, 5^4=5),
6 - 1 (6^1=6, 6^2=6, 6^3=6, 6^4=6),
7 - 4 (7^1=7, 7^2=9, 7^3=3, 7^4=1),
8 - 4 (8^1=8, 8^2=4, 8^3=2, 8^4=6),
9 - 4 (9^1=9, 9^2=1, 9^3=9, 9^4=1).

[(6374)^1793 x (625)^317 x (341)^491].
(4)^1793 x (5)^317 X (1)^491.

1793 % 4= 1 so (4)^1 = 4,
317 % 5 = 2 so (5)^2 = 5,
491 % 1 = 0 so (1)^0 = 1.

Therefore 5 x 4 x 1 = 20 here unit digit is 0 => answer.

Thank you all for explaining the answer.

I don't understand. Please explain in detail.

The easiest way to do is;

1. Check digit at the unit place,
if it is 0, 1, 5, or 6, then we will have the same digit at unit place i.e unit digit for 0 is 0, 1 is 1, 5 is 5 and for 6 is 6.

If it is 2, 3, 4, 7, 8, or 9 then divide their power by 4 and find the remainder. Put the remainder as the power of the unit place of the given number.

In this example,
For (6374)^1793.


4 is at unit place of given no., so divide 1793 by 4 as mentioned above and we get the remainder i.e. .1

Now put the remainder as a power of 4 (which is unit place of given no.), therefore, 4^1= 4 this is required unit digit.

For (625)^317.
5 is at unit place, therefore for 5 it will be the same i.e. 5

For (341)^491.
1 is at unit place, therefore required no is same i.e 1.

Now multiply 4*5*1= 20 and final unit digit is 0.

Thanks for the explanation @Channakeshava.