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What is the ones digit of 3^23 - 2^18?
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27 Jul 2017, 10:05
27 Jul 2017, 10:05
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Question Stats:
80% (01:11) correct
20% (01:17) wrong based on 90 sessions
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Re: What is the ones digit of 3^23 - 2^18?
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25 Sep 2017, 06:11
25 Sep 2017, 06:11
1
Let's use the fact that unit digits are recurrent in powers so that
31=3
32=9
33=..7
34=..1
35=..3
...
And
21=2
22=4
23=8
24=..6
25=..2
....
Thus, 321=...7 and 218=...4. Then, their difference will terminate with a 7-4=3!
31=3
32=9
33=..7
34=..1
35=..3
...
And
21=2
22=4
23=8
24=..6
25=..2
....
Thus, 321=...7 and 218=...4. Then, their difference will terminate with a 7-4=3!
Re: What is the ones digit of 3^23 - 2^18?
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25 Sep 2017, 06:30
25 Sep 2017, 06:30
3
Carcass wrote:
Now we know
Ones digit of2anypower = 2,4,8,6 i.e it keeps repeating after every 4 cycle
Ones digit of 3anypower = 3,9,7,1 i.e it keeps repeating after every 4 cycle
Now ones digit of 323 = 7 (divide 23/4 , since it repeats after every 4 cycle and the remainder is 3, so we have to consider the third term i.e 7 (3,9,7,1))
Similarly ones digit of 218 = 4 (divide 18/4 , since it repeats after every 4 cycle and the remainder is 2,
so we have to consider the second term i.e 4(2,4,8,6))
Now
the ones digit of 323−218 = 7-4 = 3
