Aptitude - Numbers - Discussion

What is unit digit ?

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 :)

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.

@Karthi
Unit digit means last digit.

Seema is right. I like her method. The way of approaching is good. Toooooo much.

@gautham. You made it very simple!

Thanks.

Why are you consider (5) the power 317 is digit unit is 5? please explain it.

Seema 's method is too good. It saves time. Thank you seema.

Unit digit means last digit..
5^(anything) is ending with 5..

So for our convenience it s considered as 5.