Q. |
What is the last digit of the number 3^{579}+ 1? |
✖ A. | 1 |
✖ B. | 3 |
✔ C. | 4 |
✖ D. | 7 |
Solution:
Option(C) is correct
Any power of 5 when divided by 4 gives a remainder 1.
Here, the power of 3 is itself a power of 5 and will give the remainder of 1 when divided by 4.
The last digit of the number will be 3.
And, hence, the last digit of the given number is $3+1 =$ 4.
Edit: For a detailed alternative solution, check comment by Deepak.
Edit 2: For yet another alternative solution, check somment by Sravan Reddy.
Sravan Reddy
()
Sreekant Singh
()
3^5^7^9 1st 9/4 R=1 , 7/4 R=3 , 5^3= 125 then 125/4 R=1 so 3^1 =3
Vivek
()
didnt get that step $3^5^--7=3^-25$
Sahil
()
3 raise to power will always give u a odd no.
and odd no. + 1 = even no.
and the only even no. in the options is 4 so the answer :-)
Deepak
()
X\Y |
1 |
2 |
3 |
4 |
5 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
1 |
1 |
1 |
1 |
1 |
2 |
2 |
4 |
8 |
6 |
2 |
3 |
3 |
9 |
7 |
1 |
3 |
4 |
4 |
6 |
4 |
6 |
4 |
5 |
5 |
5 |
5 |
5 |
5 |
6 |
6 |
6 |
6 |
6 |
6 |
7 |
7 |
9 |
3 |
1 |
7 |
8 |
8 |
4 |
2 |
6 |
8 |
9 |
9 |
1 |
9 |
1 |
9 |
y we divide y by 4? is it due to cyclicity , or ny other reason
Could have written where you writing exponents....readability is so poor. Good explanation but you have not even mentioned the exponents
Dhruv
()
Hello,
As I was going through the solution it occured to me that,
$2^5=32$
just as 3 in the above question has a power of 5 here too 2 has the power of ($5^1$)...&
32 when divided by 4 gives remainder 0 not 1..............
Just need a clarification.
Thank you for all your time and support lofoya
-a loyal consumer
if you are trying to find out the last digit of $2^5$ then divide 5 by 4 then the remainder is 1. hence unit digit is 2 thus
$2^1$ is 2..................
Key observation in this question -> Anything of power 5 is in the form of 4x+1. So the 3^5^7^9 simplifies to 3^(4x+1)
So units digit of 3^(4x+1) can be done in many ways and I like to use 'Modulus' function. Learning it helps in such cases (So,please try to learn if you find it good):
3^4 = 81 mod10 = 1 mod10
3^4x = 1 mod10
multiplying by 3 on both sides
3^(4x+1) = 3 mod10
so units digit of 3^5^7^9 = 3.. Answer is 3+1 = 4
Arithmetic way:
3^4= 81
3*4x = 81*81*81...x times. Still the units digit is 1
So answer is 3+1 = 4