CAT QUANT NUMBER SYSTEM 11

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Question 1:

How many values can natural number $n$ take, if $n !$ is a multiple of $7^{6}$ but not $7^{9}$ ?

Question 2:

If n! has 18 trailing zeros at its end, then the greatest value of n is:

Question 3:

What is the number of trailing zeroes in 20! When written in base 6?

Question 4:

How many trailing zeros are there at the end of $20 !+21 !+22 !+23 !+24 ! ?$

Question 5:

What is the $3^{\text {rd }}$ digit from right of the number $101^{76}$

Question 6:

Find the least number $\mathrm{n}$ such that no factorial has $\mathrm{n}$ trailing zeroes, or $\mathrm{n}$ + 1 trailing zeroes or $n+2$ trailing zeroes.

Question 7:

What is the highest power of 12 that divides $54 ! ?$

Question 8:

How many values can natural number $n$ take, if $n !$ is a multiple of $2^{20}$ but not $3^{20}$ ?

Question 9:

How many trailing zeroes (zeroes at the end of the number) does $60 !$ have?

Question 10:

A number $\mathrm{n} !$ is written in base 6 and base 8 notation. Its base 6 representation ends with 10 zeroes. Its base 8 representation ends with 7 zeroes. Find the smallest $n$ that satisfies these conditions. Also find the number of values of $n$ that will satisfy these conditions.
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