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2988^687,what will be the last 3 digit
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- 988=(990-2)^687
if we subtract last 3 digits of 2^687 from the last 3 digits of 990^687(which will be 000) then we get the last 3 digits of 2988^687
The last 3 digits of 2^687=8*2^684=8*16^171=8*16^(5*34+1)=16*8 i.e 128, so last 3 digits of 2988^687 is ....0000-128=872 - 10 years agoHelpfull: Yes(33) No(14)
- ans:872
period of 8 (8,4,2,6,8,4,2,6........) is 4,hence when 687 divide by 4 we will get 3 as remainder
hence for last 3 digit no we just have to calculate 88^3=(88*88)*88=44*88=872(last 3 digits) - 10 years agoHelpfull: Yes(15) No(7)
- divide 687 by 4
then rem will be 3
so 8^3 is 512
that is ans. - 10 years agoHelpfull: Yes(7) No(7)
- 592 must be the answer.
- 10 years agoHelpfull: Yes(6) No(4)
- 562 is the answer
- 10 years agoHelpfull: Yes(5) No(11)
- ans is 512
- 10 years agoHelpfull: Yes(3) No(5)
- please explain the procedure....
- 10 years agoHelpfull: Yes(2) No(0)
- Last 3 digit of the expression 2988^687 depends upon last 3 digit of 88^687. So last 3 digit of 88^687= (2*44)^687 -> = 2^687 * 44^687 -> = (2^10)^68 * 2^7 * (44^2)^343 * 44 -> = 76 * 28 * 16 * 44 -> = 1498112 .... So 112 will be the last 3 digit
- 10 years agoHelpfull: Yes(2) No(0)
- 988=(990-2)^687
if we subtract last 3 digits of 2^687 from the last 3 digits of 990^687(which will be 000) then we get the last 3 digits of 2988^687 - 10 years agoHelpfull: Yes(1) No(1)
- Unit Digit of any no. repeats after power 4n where n=0,1,2.....
Ex.:-7^1=7
7^2=9(Unit digit)
7^3=3(Unit digit)
7^4=1(Unit digit)
Unit Digit of 7^5=7 is same as 7^1=7.
i.e.in this question divide 687 by 4.then rem will be 3 so 8^3=512.
- 10 years agoHelpfull: Yes(1) No(4)
- (2^10)^68 * 2^7 * (44^2)^343 * 44
= 76 * 28 * 16 * 44(last two digits of each expression) = 1498112 .... - 10 years agoHelpfull: Yes(1) No(1)
- Take last three digits.
988^1=988
988^2=144
988^3=272
988^4=--6
last digit repeats for every 4 cycle, 687 % 4= remainder is 3
so 272 is the ans.
- 9 years agoHelpfull: Yes(1) No(0)
- 91 is the answer
- 10 years agoHelpfull: Yes(0) No(12)
- 2888^687
dividing 687 by 4 gives a remainder 3.
no 8^3= 512
so last 3 digits of 2988^687 is 512 - 10 years agoHelpfull: Yes(0) No(13)
- 192
check your windows calculator
go by options is what i can suggest
check last digit ie 2
then second last digit 88^7=92
- 10 years agoHelpfull: Yes(0) No(0)
- Answer is 984
- 10 years agoHelpfull: Yes(0) No(0)
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