Can any one help me out in finding last 3 digits of 1233^101.
thanks
(1233)101 = (1233)100 x 1233
The last three digits of the above ll depend only on 233 not anything left to that.
power last 3 digits 12332 289 12333 337 12334 521 12335 393 12336 569 12337 577 12338 441 12339 753 123310 449
Now we know 10th power of 449 is 001 ie last 3 digit of 44910 is 001 So the last 3 digit of (1233)100 = the last 3 digit of (449)10 10 = So the last 3 digit of (001)10 = 001
Thus the last 3 digits are 233
(1233)101
= (1233)100 x 1233
The last three digits of the above ll depend only on 233 not anything left to that.
Now we know 10th power of 449 is 001
ie last 3 digit of 44910 is 001
So the last 3 digit of (1233)100 = the last 3 digit of (449)10 10 = So the last 3 digit of (001)10
= 001
Thus the last 3 digits are 233