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# What is the units digit of (8^8) / 2? can someone give me

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CEO
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What is the units digit of (8^8) / 2? can someone give me [#permalink]

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14 Nov 2007, 15:08
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

What is the units digit of (8^8) / 2?

can someone give me the shortcut?
Intern
Joined: 18 Jun 2007
Posts: 7
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Kudos [?]: 3 [0], given: 0

Re: units digit - 8^8 [#permalink]

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14 Nov 2007, 16:29
bmwhype2 wrote:
What is the units digit of (8^8) / 2?

can someone give me the shortcut?
Here is mine:

Unit digits of the following

8^1 = 8
8^2 = 4
8^3 = 2
8^4= 6
8^5 =8

At 8^5, the unit digit go back to 8, so I know the pattern is 8 4 2 6.

I stop there and count the power to the pattern, power of 8 lands on 6

Hope it helps.

Someone has a faster way?
Intern
Joined: 06 Oct 2007
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Kudos [?]: 1 [0], given: 0

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14 Nov 2007, 16:50
My trick is to just multiply the units digit.

For example 8*8= 64 and 4*4=16

So for 8^8 Units digit will be 6

Since this 6 was derived from 6*6 = 36

Then divide it by 2 and that gives you 18

So the units digit should be 8.

Just make sure you keep track of the tens digit as well.

I know its kinda awkward, but it helps me!!

Let me know if you need a more detailed explination.

~ Ev
CEO
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Location: New York City
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18 Nov 2007, 04:27
Ev123 wrote:
My trick is to just multiply the units digit.

For example 8*8= 64 and 4*4=16

So for 8^8 Units digit will be 6

Since this 6 was derived from 6*6 = 36

Then divide it by 2 and that gives you 18

So the units digit should be 8.

Just make sure you keep track of the tens digit as well.

I know its kinda awkward, but it helps me!!

Let me know if you need a more detailed explination.

~ Ev

CEO
Joined: 21 Jan 2007
Posts: 2747
Location: New York City
Followers: 11

Kudos [?]: 941 [0], given: 4

Re: units digit - 8^8 [#permalink]

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18 Nov 2007, 04:28
jasminebloom wrote:
bmwhype2 wrote:
What is the units digit of (8^8) / 2?

can someone give me the shortcut?
Here is mine:

Unit digits of the following

8^1 = 8
8^2 = 4
8^3 = 2
8^4= 6
8^5 =8

At 8^5, the unit digit go back to 8, so I know the pattern is 8 4 2 6.

I stop there and count the power to the pattern, power of 8 lands on 6

Hope it helps.

Someone has a faster way?
this is the way i did it also.

the original question was
what is the units digit of (8^6)/2
Director
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Re: units digit - 8^8 [#permalink]

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18 Nov 2007, 05:36
bmwhype2 wrote:
What is the units digit of (8^8) / 2?

can someone give me the shortcut?

I believe the answer is 3.

8^8 = (2^3)^8 = 2^24 = 4^12 (I converted it into a base of 4 because finding the units digit in the base of 4 is simple; it is 4 if the power is odd and 6 if the power is even)

units digit of 4^12 = 6
a number with units digit 6 when divided by 2 will give a units digit of 3.
Director
Joined: 26 Feb 2006
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Re: units digit - 8^8 [#permalink]

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18 Nov 2007, 12:44
jasminebloom wrote:
bmwhype2 wrote:
What is the units digit of (8^8) / 2?

can someone give me the shortcut?
Here is mine:

Unit digits of the following

8^1 = 8
8^2 = 4
8^3 = 2
8^4= 6
8^5 =8

At 8^5, the unit digit go back to 8, so I know the pattern is 8 4 2 6.

I stop there and count the power to the pattern, power of 8 lands on 6

Hope it helps.

Someone has a faster way?

you did it. thats clear enough; nothing to add.
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 3978 [0], given: 360

Re: units digit - 8^8 [#permalink]

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18 Nov 2007, 13:02
8.

GK_Gmat wrote:
a number with units digit 6 when divided by 2 will give a units digit of 3.

incorrect.
06 /2 =>3
16 /2 =>8
26 /2 =>3
36 /2 =>8

8^8/2=4*8*8^6=2*4^3=2*4=8

3 is a trap.
Director
Joined: 26 Feb 2006
Posts: 901
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Kudos [?]: 123 [0], given: 0

Re: units digit - 8^8 [#permalink]

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18 Nov 2007, 13:38
bmwhype2 wrote:
What is the units digit of (8^8) / 2?

can someone give me the shortcut?

walker wrote:
8.

GK_Gmat wrote:
a number with units digit 6 when divided by 2 will give a units digit of 3.

incorrect.
06 /2 =>3
16 /2 =>8
26 /2 =>3
36 /2 =>8

8^8/2=4*8*8^6=2*4^3=2*4=8

3 is a trap.

thats an interesting point.

= 8^8/2 = (2^3)^8/2 = 2^24 / 2 = 2^23

2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6
2^5 = 32

using the pattren above, 2^23 shoulkd have 8 in unit digit.
CEO
Joined: 17 Nov 2007
Posts: 3586
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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18 Nov 2007, 13:53
3 also can be exclude because 8^8/2 must be even.
18 Nov 2007, 13:53
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