BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

knewton ps

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 156
Joined: Sat Sep 04, 2010 2:27 am
Location: Leeds,UK
Thanked: 1 times

by lokesh r » Thu Sep 09, 2010 6:51 am
Finding units digit of 13^77 is as good as finding units digit of 3^77.

Using famous rule, units digit of

3^1=3,3^2=9,3^3=7,3^4=1,

3^5=3......

77=4x19+1

Units digit of 13^77= Units digit of 3^77=3
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 324
Joined: Mon Jul 05, 2010 6:44 am
Location: London
Thanked: 70 times
Followed by:3 members

by kmittal82 » Thu Sep 09, 2010 6:59 am
Let list some units digts of 3

3,9,7,1,3,9,...

We see a repetition every 4 intervals (3^1 has same digit at 3^5, 3^2 has same as 3^6 etc..)

Thus, 3^77 will have same as 3^73, which in turn has same as 3^69

77=4x19 + 1, so it will have the units digit of 3^(4+1) = 3^5 = 3
Top
Post new topic Post Reply
• Page 1 of 1