Numbers questions

Question

find the attached question.

puneetj · Answer

reminder is 8

you need to use the cyclicity properties of numbers

3^1 will end in = 3
3^2 will end in= 9
3^3 will end in= 7
3^4 will end in= 1
3^5 will end in = 3

....

so 3^21 will end in 3

Similarly
6^1 will end in 6
6^2 will end in 6

so 6^55 will ALWAYS end in 6

So 3^21 * 6^55 will always end in 8 (3*6)

So the reminder when divided by 10 will always be 8

pkmme · Answer

the answer is correct.

puneetj · Answer

pkmme - Don't be shy to give a kudos then 8-)

sudhir18n · Answer

given u njoy:)
 its 8
i use CRT method

3^21*6^55/10

(3^2)10*3 *6^55
(-1)^10*3*6/10
18/10 =8

Spidy001 · Answer

when a number is divided by 10 , last digit is the remainder.

so we have to find the unit digit of the given expression

( 3^(21)*6^(55))/10

3 has cyclicity of 4 => 3^(21) will have same unit digit as 3^1 = 3

unit digit of 6^any positive number = 6

=> remainder of ( 3^(21)*6^(55))/10 = remainder of (3*6/10) = remainder of (18/10)

= 8

puneetj · Answer

Thank you Sudhir....still waiting for a one from pkmme

amit2k9 · Answer

3 with exponential power raised repeats after 4.

thus 3^21 will have units digit = 3
also, 6 with exponential power raised will always provide 6 in the units digit.

thus, 3*6 = 18.

remainder = 8.

Prep Toolkit