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

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What is the units digit of (8^8) / 2? can someone give me [#permalink]  14 Nov 2007, 14:08
What is the units digit of (8^8) / 2?

can someone give me the shortcut?
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Re: units digit - 8^8 [#permalink]  14 Nov 2007, 15:29
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?
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[#permalink]  14 Nov 2007, 15:50
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
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[#permalink]  18 Nov 2007, 03:27
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

u made a calculation error.
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Re: units digit - 8^8 [#permalink]  18 Nov 2007, 03:28
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]  18 Nov 2007, 04:36
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
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Re: units digit - 8^8 [#permalink]  18 Nov 2007, 11:44
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
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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Re: units digit - 8^8 [#permalink]  18 Nov 2007, 12:02
Expert's post
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
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Re: units digit - 8^8 [#permalink]  18 Nov 2007, 12:38
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
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Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
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[#permalink]  18 Nov 2007, 12:53
Expert's post
3 also can be exclude because 8^8/2 must be even.
[#permalink] 18 Nov 2007, 12:53
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# What is the units digit of (8^8) / 2? can someone give me

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