The unit place digit in 17^789

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11 Apr 2011 unit place?

The unit place digit in 17^789

OPtion

1) 1
2) 2
3) 3
4) 4
5) 5
6) 6
7) 7
8) 8
9) 9
10) 0

Solution

7

Correct Option: 7 Best Solution (7)

Karthick Babu   13 years AGO

Unit places:
7^1=7
7^2=9
7^3=3
7^4=1
7^5=7
7^6=9....again repeated.So length of cycle is 4
789/4=197 and remainder is 1.
Therefore 7^1 is =7. The Option 7

Like? Yes (5) | No   

sanjeev   13 years AGO

break (17)^789) as (17)^700 * (17)^80 * (17)^9

(17)^700 = ((17)^4)^175) has unit digit will be 1
(17)^80 = ((17)^4)^20) has unit digit will be 1
(17)^9 = (17)^8 * (17)^1
=((17)^4)^2) * (17)^1
now as we know (17)^4 has unit digit will be 1
and last (17)^1 has unit digit as 7
so finally multiplying unites digits
= (17)^80*(17)^4 * (17)^4 * (17)^1
1 * 1 * 1 * 7
= unit digit will be 7

Like? Yes (4) | No (1)  

Seema   13 years AGO

7,9,3,1 are 4 rpeating sequence of unit digit
789%4=1
so unit digit is 7

Like? Yes (3) | No (1)  

Balakumaran N.A   13 years AGO

17^1=7(unit digit) 17^2=9 17^3=3 17^4=1, etc.

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ULAGUNATHAN   13 years AGO

unit place of multiple of 7 is 7,9,3,1. so the 9th times the number 7 is appear. so the answer is 7

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gopi uttarakavatam   13 years AGO

unit place:
7^1=7;
7^2=9;
7^3=3;
7^4=1;7^5=7;.....so on..but 789 =4*197+1 so unit place will be 7

Like? Yes (1) | No   

pradeep kumar   13 years AGO

we can simply check it by cyclicity rule..

Like? Yes (1) | No