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CAT 1998 Question(Number System – Finding the Unit digit of power of 2)

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Q.)What is the digit in the unit’s place of ${2}^{51}$?
A)2
b)8
c)1
d)4

Solution :

${2}^{4}$ = 16

Any power of 16 is always going to last with unit digit as 6.

So, ${2}^{51}$ can be written as

${2}^{51}$ = ${ { (2 }^{ 4 } })^{ 12 }X{ 2 }^{ 3 }$

= ${ (16 })^{ 12 }X{ 8 }$

So, ${ (16 })^{ 12 } $ would last with unit digit as 6 and then multiplied with 8 will result in unit digit as 8.

Hence , unit’s place of ${2}^{51}$ = 8

OPTION(B)