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

• 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
• 12 years agoHelpfull: Yes(2) No(0)
• 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
• 12 years agoHelpfull: Yes(0) No(1)
• ans is 3
  logic of this question is the power values's last digit
• 12 years agoHelpfull: Yes(0) No(0)
• 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
• 8 years agoHelpfull: Yes(0) No(0)