5000! = 5000*4999*4998*4997*...*3*2*1.

Of all the numbers up to 5000, there are 5000/7 = 714 numbers that have 7 as a factor.
Of these 714, 714/7 = 102 of them have 7² as a factor.
Of these 102, 102/7 = 14 of them have 7³ as a factor.
Of these 14, 14/7 = 2 of them have 7⁴ as a factor.

Adding all of these gives 832, so that is the highest power of 7 in 5000!.

There's a formula:
The higest power of p(prime) that divides n! is exactly:

Last edited by krassi_holmz (2006-03-01 05:02:59)

6^2=3^2 2^2
a=3*11^2

NT # 3

A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before he will have a result that will end with 3 zeroes?

Correct!

105/4

What?
105/4=3/8*70=3/8*(2*5*7)
105/4=5/36*189=5/36*(3*3*3*7)
105/4=7/72*270=7/72*(2*5*3*3*3)
105/4=15/96*168=15/96*(7*3*2*2*2)
There ISN"T a number LESS than 105/4

NT # 5

In an examination, the average marks obtained by students who passed was x%, the average marks obtained by students who failed was y% and the average marks of all the students who appeared for the examintion was z%. Find the percentage of students who failed in the examination in terms of x, y, and z.

I concede, you are correct krassi_holmz, well done!

Want help to solve few questions...simple for people having knowledge of Euler/ Fermet theorem but i am not that great at it...

1) Two numbers 698 and 450 when divided by a certain divisor leave remainders of 9 and 8 respectively. Find the largest such divisor.

What is the minimum number of identical square tiles required to completely cover a floor of dimensions 8m 70 cm by 6m 38cm

ok learnt the approach the HCF will be 58 and not 29 so the answer will be 870*638/58^2 = 165

thnx anyway