Number Theory

Jai Ganesh · 2006-02-28 04:13:03

NT # 1

What is the highest power of 7 in 5000!?

mathsyperson · 2006-02-28 04:21:32

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 7[sup]4[/sup] as a factor.

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

Jai Ganesh · 2006-02-28 04:28:26

krassi_holmz · 2006-02-28 06:02:06

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

Last edited by krassi_holmz (2006-02-28 06:02:59)

Jai Ganesh · 2006-02-28 20:18:25

NT # 2

If both 11² and 3³ are factors of the number a * 4³ * 6² *13[sup]11[/sup], then what is the smallest possible value of a?

krassi_holmz · 2006-02-28 20:23:06

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

Jai Ganesh · 2006-02-28 23:49:56

krassi_holmz, you get this award!

Jai Ganesh · 2006-03-01 00:00:53

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?

krassi_holmz · 2006-03-01 02:24:09

20*21*23*24*25=127512000.

Jai Ganesh · 2006-03-01 03:36:47

Correct!

Jai Ganesh · 2006-03-01 20:48:23

NT # 4

What is the Least Common Multiple of 3/8, 5/36, 7/72 and 15/96?

krassi_holmz · 2006-03-02 02:25:02

105/4

Jai Ganesh · 2006-03-02 02:48:20

krassi_holmz · 2006-03-02 03:15:37

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

Jai Ganesh · 2006-03-02 03:36:49

krassi_holmz,

What about 105/288?

Jai Ganesh · 2006-03-02 17:53:35

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.

krassi_holmz · 2006-03-03 00:06:29

for NT 4:
(105/288):(3/8)=(35/36), which is not an integer???

Jai Ganesh · 2006-03-03 02:29:58

I concede, you are correct krassi_holmz, well done!

dan howitt · 2008-06-02 05:19:13

ganesh wrote:

krassi_holmz, you get this award!
http://www.greetingcards.fimark.net/job-well-done.jpg

Nice!

Sudeep · 2008-07-21 14:35:10

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.

ZHero · 2008-07-21 14:59:00

If upon dividing 698 and 450, the divisor leaves remainders 9 and 8 respectively then it Must divide (698-9=689) and (450-8=442)!
Therefore, the required number is HCF of (689=13*53) and (442=2*13*17) which clearly is 13 !
Hence 13 is the answer...

Sudeep · 2008-07-21 21:37:22

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

ZHero · 2008-07-21 23:05:43

Hi BumBumBhole!
From India haan?
Well.. Me too!
Jai Shiv Shankar!

Coming to the point..
Minimum number of squares will be needed if their size is maximum!
So required size of the squares is the square with sides of length which is HCF of 870cm & 638cm i.e. 29cm !
And number of squares is area of floor divided by area of tile..
=(870*638)/(29*29)
=330

Easy! Ain't it?

Last edited by ZHero (2008-07-21 23:30:05)

Sudeep · 2008-07-22 00:52:38

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

thnx anyway

Sudeep · 2008-07-22 01:00:34

Another one ...the total number of factors of a natural number N is 45. What is the maximum number of prime numbers by which N can be divided?

Math Is Fun Forum

#1 2006-02-28 04:13:03

Number Theory

#2 2006-02-28 04:21:32

Re: Number Theory

#3 2006-02-28 04:28:26

Re: Number Theory

#4 2006-02-28 06:02:06

Re: Number Theory

#5 2006-02-28 20:18:25

Re: Number Theory

#6 2006-02-28 20:23:06

Re: Number Theory

#7 2006-02-28 23:49:56

Re: Number Theory

#8 2006-03-01 00:00:53

Re: Number Theory

#9 2006-03-01 02:24:09

Re: Number Theory

#10 2006-03-01 03:36:47

Re: Number Theory

#11 2006-03-01 20:48:23

Re: Number Theory

#12 2006-03-02 02:25:02

Re: Number Theory

#13 2006-03-02 02:48:20

Re: Number Theory

#14 2006-03-02 03:15:37

Re: Number Theory

#15 2006-03-02 03:36:49

Re: Number Theory

#16 2006-03-02 17:53:35

Re: Number Theory

#17 2006-03-03 00:06:29

Re: Number Theory

#18 2006-03-03 02:29:58

Re: Number Theory

#19 2008-06-02 05:19:13

Re: Number Theory

#20 2008-07-21 14:35:10

Re: Number Theory

#21 2008-07-21 14:59:00

Re: Number Theory

#22 2008-07-21 21:37:22

Re: Number Theory

#23 2008-07-21 23:05:43

Re: Number Theory

#24 2008-07-22 00:52:38

Re: Number Theory

#25 2008-07-22 01:00:34

Re: Number Theory

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