Latest self Aptitude Question SOLUTION: find the last digit of 7^2003. a.)1 b).3 c.)7 d.)9

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(#M40004128) SELF question Keep an EYE

find the last digit of 7^2003.
a.)1 b).3 c.)7 d.)9

ajay (12 years ago)

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Dr.Dipin Singh  (12 years ago)

7^1=7
7^2=49
7^3=343
7^4=2401

so 7^4n is having unit digit as 1.
2003 = 4*500 +3
7^2003 = 7^(4*500 +3 )

so 7^2003 is having same digit at unit place as 7^3 which is 3.

so option b

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Sanjana Patnaik  (12 years ago)

The cyclicity of 7 is 4(i;e 7^1=7. 7^2=49, 7^3=343, 7^4=2401)
Thus 7^2003 can be written as 7^2000+3
Thus the unit digit of 7^3 would be 3
Answer option is 3

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srilatha  (12 years ago)

ans is 3
logic of this question is the power values's last digit

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Asha Verma  (8 years ago)

b option is correct . To check divide the power 2003 by 4 .then see what the remainder is , here the remainder is 3 . Then the last digit of base will be raised to the power as many times as the remainder . Here 7^3=343. The unit digit of this is the unit digit of given number

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