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Product of the Integers

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Product of the Integers

by money9111 » Mon Feb 01, 2010 8:20 pm
If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of P?

a. 10
b. 12
c. 14
d. 16
e. 18

I immediately started thinking "factorials" which i'm not a fan of... I know this problem has to be easier than that though...

OA C
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by thephoenix » Mon Feb 01, 2010 8:35 pm
product of 1....to 30=30!
trick to solve

p!/n^k
is
div p/n and write the quotient

div the quotient by n and again write the quo

repeat till u get 1 as quo

add all the quo thats the ans

30/3---->10
10/3---->3.333(always take int value less than the value u get)
3/3----->1

10+3+1=14
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by money9111 » Mon Feb 01, 2010 8:43 pm
the phoenix, i'm not sure I understand this solution
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by papgust » Mon Feb 01, 2010 9:40 pm
The question basically asks how many 3's are there in 30!. 30! = 1*2*...30

Find out the numbers that have 3's.

3 --> 1 3's
6 --> 1 3's
9 --> 2 3's
12--> 1 3's
15--> 1 3's
18--> 2 3's (3*3*2)
21--> 1 3's
24--> 1 3's
27--> 3 3's (3*3*3)
30--> 1 3's

Totally 14 3's. (C)
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by money9111 » Mon Feb 01, 2010 10:27 pm
aaahhhh ok.... now that makes sense
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by ajith » Mon Feb 01, 2010 11:44 pm
money9111 wrote:If p is the product of the integers from 1 to 30, inclusive, what is the greatest integer k for which 3^k is a factor of P?

a. 10
b. 12
c. 14
d. 16
e. 18

I immediately started thinking "factorials" which i'm not a fan of... I know this problem has to be easier than that though...

OA C
there are 10 multiples of 3
3 multiple of 9
and 1 multiple of 27

so, 3^14 is the highest power 0f 3 which is a factor of 30!
so C
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