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How to find units digit of powers?

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Intern
Joined: 11 Sep 2013
Posts: 1
How to find units digit of powers?  [#permalink]

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06 Sep 2017, 20:31
1
1
UNITS DIGIT OF ANY INTEGER
Hi peeps,
While preparing I noticed this and thought it will be useful to all. Not sure if someone has already posted it.

For instance what is the units digit of 567^996? The unit digit depends only on the unit digit of the original number. here "7". Refer the table below: As 996 is a multiple of 4, we ca find that the unit digit of 567^996 is 1.

UNITS DIGIT OF ANY INTEGER with INTEGER POWERS (1,2,3...)

1 = Always 1
2 = 2, 4, 8, 6 repeats
3 = 3, 9, 7, 1 repeats
4 = 4 , 6 repeats
5 = Always 5
6 = Always 6
7 = 7, 9, 3, 1 repeats
8 = 8, 4, 2, 6 repeats
9 = 9, 1 repeats
10 = always 0
Math Expert
Joined: 02 Sep 2009
Posts: 47161
Re: How to find units digit of powers?  [#permalink]

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13 Sep 2017, 09:41
EvenPrime wrote:
UNITS DIGIT OF ANY INTEGER
Hi peeps,
While preparing I noticed this and thought it will be useful to all. Not sure if someone has already posted it.

For instance what is the units digit of 567^996? The unit digit depends only on the unit digit of the original number. here "7". Refer the table below: As 996 is a multiple of 4, we ca find that the unit digit of 567^996 is 1.

UNITS DIGIT OF ANY INTEGER with INTEGER POWERS (1,2,3...)

1 = Always 1
2 = 2, 4, 8, 6 repeats
3 = 3, 9, 7, 1 repeats
4 = 4 , 6 repeats
5 = Always 5
6 = Always 6
7 = 7, 9, 3, 1 repeats
8 = 8, 4, 2, 6 repeats
9 = 9, 1 repeats
10 = always 0

More on this:

8. Exponents and Roots of Numbers

Cyclicity and the remainders on the GMAT
Units digits, exponents, remainders problems
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Re: How to find units digit of powers? &nbs [#permalink] 13 Sep 2017, 09:41
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How to find units digit of powers?

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