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

• 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..
• 12 years agoHelpfull: Yes(4) No(2)
• 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
  
• 11 years agoHelpfull: Yes(2) No(0)
• 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)
  
  
• 12 years agoHelpfull: Yes(0) No(1)
• 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
• 11 years agoHelpfull: Yes(0) No(0)
• (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
  
  
• 11 years agoHelpfull: Yes(0) No(0)