Problem Solving

greatest 3 digit prime of 2000c1000

Let me post the complete question with answers to this question. This will help in better understanding.

Q.What is the largest 3 digit prime factor of the integer 2000C1000?
OPTIONS
1)661
2)211
3)733
4)859
5)None of these

For obtaining largest prime factor, divide 2000 by 1,2,3,4,5... n
1 and 2 are eliminated as when 2000 is divided by these nos, we'll get a 4-digit answer.
So the largest no will be obtained by dividing 2000 by 3.
Thus, 2000/3=667.

Hence the nearest prime no possible is less than 667.
Taking the nos one by one then we can eliminate 666,665,664,663,662.
661 is the biggest 3-digit prime number.
The range is also satisfied since 661*3=1983<2000

Thus, ans is [spoiler]Option:A[/spoiler]