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desh kumar

· started a discussion

· 1 Months ago

a (Question: 200912.0 )

ans c

Question:
When 233 is divided by 10, then the remainder will be —
Options:
A) 2
B) 3
C) 4
D) 8
Solution:
Ans: (a) 

Unit place of 233 is 2. So when number is divided by 10, then remainder will be 2. 

sawan kumar

· commented

· 1 Months ago

hmm

Knowledge Expert

· commented

· 1 Months ago

Dear Student,

2 is the required answer.

Its common to all that the remainder of any number when divided by 10 is it's unit digit.
Therefore, finding the remainder of 2^33 when divided by 10 is equivalent of finding the unit digit of 2^33.
Let U(x ) be a function which gives out the unit digit of x.
Now, we observe

U(2^1)=2

U(2^2)=4

U(2^3)=8

U(2^4)=6

U(2^5)=2

……………

Therefore this pattern continues.

Every 4th power ends with 6 and the next one 2.

33=4×8+1

Hence , the number ends with 2.

Consequently, the remainder and the required answer is 2.

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