(Q). Find the highest power of 1000 in 1000×1001×1002×1003×………..till 1000 terms.
Solution:-
=
now 1000 = 10×10×10 = 2³×5³
So to find maximum power of 1000 we need to find maximum power of 5 first & then divide that value by 3 (due to 5³) and Integer part of that value will be the final answer.
Hence highest power of 5 in
∴ Highest power of 5 in = 496 – 246 = 250
Hence highest power of 5³ in =
= 83
Hence highest power of 1000 in Given question = 83 Answer