Aptitude - Numbers - Discussion

Very good explanation, Thanks all.

Thanks All for explaining the answer.

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.

Thanks for the explanation @Channakeshava.

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.

I don't understand. Please explain in detail.

Thank you all for explaining the answer.

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.

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.

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.