Carcass wrote:
\(P=23^{25}-23\). What is the unit digit of \(P\) ?
A. 0
B. 1
C. 3
D. 7
E. 9
Kudos for the right answer and explanation
Here,
First we need to know the power of 3
\(3^1 = 3\) --------------unit digit = 3
\(3^2 = 9 \)--------------unit digit = 9
\(3^3 = 27\) --------------unit digit = 7
\(3^4 = 81\) --------------unit digit = 1
\(3^5 = 243\) --------------unit digit = 3
We can see in the power of 3, unit digit repeats after 3, 9, 7, 1. we have 4 terms
As per ques, it is given \(23^{25}\)
just concentrate with the unit digit 23 i.e
3.
since, after every 4th term in the power of 3, repeats itself i.e 3,9,7,1,
3so, divide \(\frac{25}{4} \) and the reminder is 1, (
25 is the power of 23, given in the ques. If the power is 36 then we divide 36 by 4)
that means we need the 5th term
the 5 term from the 3,9,7,1,
3 will be 3 (unit digit),
similarly, 6th term will be 9,
7th term will be 7
8th term will be 1 and so on...........
so, the unit digit for \(23^{25}\) = 3
and we know 3 -3 = 0 , so the unit digit for \(P=23^{25}-23 = 0 \)