Latest Book Aptitude Question SOLUTION: What is the unit digit in {(6374)^1793 x (625)^317 x (341)^491}?

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What is the unit digit in {(6374)^1793 x (625)^317 x (341)^491}?

Asked In Book Ratan Lal Jat (12 years ago)

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naagar  (12 years ago)

the last digit of (625)^317 will be 5....
last digit of 341^491 will be 1
last digit of 6374 may be 0,2,4,6,8
when it will get multiplied by 5 then last digit will be 0 only..

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sanjay  (11 years ago)

unit digit of a product of n numbers is same as the unit digit in the product of unit digit of each number
so unit digit of (6374)^1793=>unit digit of 4^1793= 4
unit digit of (625)^317=>unit digit of 5^317= 5
unit digit of (341)^491=>unit digit of 1^491= 1
so unit digit=>unit digit of 4*5*1 = unit digit of 20 => 0 is the unit digit

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mohd zubair khan  (12 years ago)

it can be solved as follows
4^1793 x 5^317 x 1^491 (take last digit of each term)
{4 x (4^4)^448} x {5 x (5^4)^79} x {1^3 x (1^4)^122}
{convert each term in its 4n form}
{4 x 4} x {5 x 5} x 1
16 x 25
6 x 5
30
so unit digit is 0. (your feedback is valuable to me)

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gobinath  (11 years ago)

4^1=4
4^2=16 6
4^3 64 4
1793==some +1
4*4=16 6
5^any thing 5
1^anything 1
6*5=30 unit digits 0

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RAKESH  (11 years ago)

(6374)^1793=(2*3187)^1793=2^3187*3187^1793
last digit of 2^3187 will be 8
last digit of 3187^1793 will be 7
last digit of (625)^317 will be 5
last digit of 341^491 will be 1
unit digit will be 8*7*5*1=280
unit digit will be 0

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