Question

Highest Power of 3 in 80! is :

a) 36
b) 34
c) 23
d) 24

Please teach the technique to tackle these types of Problems..

Answer 1

@mukushla

Answer 2

The p adic order of n! is given by, $$v_p(n!)=\sum_{j\leq \log_p(n)}[\frac{n}{p^j}]$$

Answer 3

What to do with this, can you please guide me?

Answer 4

@waterineyes I was reading over at the site: http://byjusclasses.com/arithmetic/2/
and saw the attached statement.

Answer 5

Here waterineyes

Answer 6

For a prime p, define v_p(n) as the highest power of p that divides n

Answer 7

I am unable to see the whole document.. @Directrix

Answer 8

So, I tried out the technique on finding the greatest power of 2 in 6! and the technique worked. But, I do not know why it works.

I also ran 80! and the greatest power of 3 through the technique and did get one of the options you posted.

Answer 9

Do you see why $$v_p(ab)=v_p(a)+v_p(b)$$

Answer 10

@Directrix you can try if you think right and tell me if it worked..

Answer 11

@waterineyes To see the entire document, click on the URL: http://byjusclasses.com/arithmetic/2/

Answer 12

@waterineyes If you cannot get the web page to come up, I will snip the entire page for you and post it here.

Answer 13

How much number theory do you know

Answer 14

I got it @Directrix

Quite useful it is.. Thank you buddy..

Answer 15

I know some of it..

Wait, I start a new post, there you will teach me,. Okay??

Answer 16

Uhm ok