Question

Find the no. or positive integer which divides 10^999 but not 10^998.

Answer 1

10^999=2^999×5^999
10^998=2^998×5998
Now, 10^999 wil be divisible by 2^0×5^999 but not 10^998,similarly 2^1×5^999,2^2×5^999....
Thus, there will be 1000 positive intgers.Similarly, we can do for 2^999×5^0...It will have 999 numbers since 2^999 and 5^999 are already counted in above.Thus in total it has (1000+999)=1999 factors.

Answer 2

Answer:

1999 factors.

Step-by-step explanation:

Given, 10⁹⁹⁹ = 2⁹⁹⁹ × 5⁹⁹⁹

           10⁹⁹⁸ = 2⁹⁹⁸ × 5⁹⁹⁸

Now, 10⁹⁹⁹ will be divisible by 2⁰ × 5⁹⁹⁹ but 10⁹⁹⁸ will not be divisible.

Similarly, 2¹ × 5⁹⁹⁹, 2² × 5⁹⁹⁹,....... will divide 10⁹⁹⁹.

Then there will be 1000 positive integers.

Similarly, 2⁹⁹⁹ × 5⁰, 2⁹⁹⁹ × 5¹, 2⁹⁹⁹ × 5²,.......2⁹⁹⁹ × 5⁹⁹⁸.

It will have 999 numbers since 2⁹⁹⁹ × 5⁹⁹⁹ is already counted above.

Thus, in total it has 1000 + 999 = 1999 factors.