1. Prove that 3^10 divides 30! Which is highest natural number n such that 3^n divides 30!.
Answers
Answer:
To find the largest integer n which divides 33!,
First we find the multiples of 2 which are less than 33!.
16 multiples of 2 are less than 33!.
So in 33!, all these 16 numbers will contribute one power of 2.
Similarly, all multiples of 4 will contribute one extra power each.
Similarly for multiples of 23,24,25.
Number of Multiples of 22 less than 33! are 8.
Number of Multiples of 23 less than 33! are 4.
Number of Multiples of 24 less than 33! are 2.
Number Multiple of 25 less than 33! is 1.
Next we add all these numbers to get the largetst power of 2 in 33!
=16+8+4+2+1=31
In terms of notation
Largest power of 2 in 33!
=[233]+[433]+[833]+[1633]+[3233] (where [.] denotes greatest integer function)
=16+8+4+2+1
=31
hope it will help
Answer:
this is your Ans
Step-by-step explanation:
plz follow me
