So as per problem units number must be the result of
(4^1793)*(5^317)*(1^491)
From the above calculations done it is evident that
1^anything =1 and 5^any positive number gives 5 as units digit
Similarly with 4 powers
Now take 4^1793.......First divide the power 1793/4 gives remainder 1.
So Units digit is (4^1)*5*1=20 whose
units digit is 0
Emela said:
(Thu, Jun 9, 2011 05:22:24 AM)
How can you divide 1793 simply by 4 and write that remainder? is it applicable for any number like 6^, 7^.
Pratiksha said:
(Wed, Jun 29, 2011 08:05:24 AM)
What is unit digit ?
Shubhi said:
(Sun, Jul 3, 2011 09:16:25 AM)
The unit digit is simply another term for the ones place..
the unit digit in 2343546 is 6
the unit digit in 234 is 4.. etc :)
Goutham said:
(Mon, Jul 4, 2011 10:57:01 AM)
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.
Remember, all digits at the power of 5 gives the value having unit place containing the original digit. Special digits (0,1,5,6) raised to any power always give the value having unit place containing the original digit.
In this, 1793/5= ### and remainder is 3,
Unit value of 6374 is to be raised to power of 3 = 4^3= Unit value is 4.
Similarly 317/5= ### and remainder is 2,
Unit value of 625 is to be raised to power of 2 = 5^2= Unit value is 5.
Last factor comes in special digit i.e. 1 and will always give 1 at unit place,if raised to any power.
Hence, the unit place of the result will be 4x5x1= 20; 0 at unit place.
Vasanthi said:
(Fri, Jul 15, 2011 07:58:47 AM)
@Karthi
Unit digit means last digit.
Gaurav said:
(Sat, Jul 23, 2011 11:03:08 AM)
Seema is right. I like her method. The way of approaching is good. Toooooo much.
Shashank said:
(Tue, Sep 20, 2011 05:04:19 PM)
@gautham. You made it very simple!
Thanks.
Dharmraj said:
(Sun, Oct 16, 2011 11:00:47 AM)
Why are you consider (5) the power 317 is digit unit is 5? please explain it.
Swetha said:
(Fri, Nov 4, 2011 04:39:37 PM)
Seema 's method is too good. It saves time. Thank you seema.
Aruna said:
(Thu, Dec 1, 2011 07:20:28 PM)
Unit digit means last digit..
5^(anything) is ending with 5..
So for our convenience it s considered as 5.
Abc said:
(Sat, Dec 17, 2011 04:50:48 PM)
This can be done in a simpler manner.
The unit digit of 625^x is 5.
The unit digit of 6374^y is an even number.
When multiplied, the unit digit must be 0.
How?
Sasi said:
(Tue, Dec 27, 2011 02:22:18 PM)
When finally mutilpled (4*5*1) we get 20. Consider the 20, the last digit ill be the unit digit. So the answer is 0,
