24600

Question

what to do in this problem?

sgmuthukumar · Answer

goyalsau wrote:what to do in this problem?

Lets breakdown the number.

264600=2646*100
=1323*2*5*5*2*2
=441*3*.....
=21*21*3*....
=7*3*7*3*3*2*5*5*2*2
=7^2*3^3*2^3*5 ^2

For a number to be not divisible by 6, it should not be divisible by 3,therefore

Power or 7=2
Power of 3=2
Power of 2=3
Power of 5=2

To get the total number

3*3*4=36

pradeepkaushal9518 · Answer

i dont understand 3*3*4

lilisanei · Answer

To obtain the number of divisors, first break the number into the prime factors, and then add one unit to the power of each prime factor and obtain their product to get the number of divisors.

for this example after omitting factor of 3, we have 7^2 and 5^2 and 2^ 3, so our powers are 2,2, and 3, after adding one unit to each one, we have, 3 ,3 , 4 and our final answer: 3x3x4=36

sgmuthukumar · Answer

sgmuthukumar wrote:goyalsau wrote:what to do in this problem? Lets breakdown the number. 264600=2646*100 =1323*2*5*5*2*2 =441*3*..... =21*21*3*.... =7*3*7*3*3*2*5*5*2*2 =7^2*3^3*2^3*5 ^2 Power or 7=2 Power of 3=2 Power of 2=3 power of 5=2 For a number to be not divisible by 6, it should not be divisible by 3,therefor To get the total number 3*3*4=36 The product of any combination of 7,3,2, and 5 will be a divisor of 264600. For example (7^1)*(3^2)*(2^3)*(5^0)[504] will be a divisor of 264600(264600/504=525)... therefore the powers of 7 can be 0,1,2. powers of 3=0,1,2. powers of 2=0,1,2,3. powers of 5=0,1,2. For a number to be not divisible by 6, it should not be divisible by 3. Hence the number 3 is omitted. 3 powers of 7* 3 powers of 5* 3 powers of 2 gives us 36. hope this helps you !!

goyalsau · Answer

Well Guys Correct Answer is 63.

Rahul@gurome · Answer

Solution:
264600 = (2^3) * (3^3) * (5^2) * (7^2).

Now we need only those factors that don’t have powers of both 2 and 3 in them because they will combine to give 6. But these factors can contain either only powers of 2 or only powers of 3.

See the table:
1------------1---------1
2------------5---------7
(2^2)------(5^2)----(7^2)
(2^3)
3
(3^2)
(3^3)

Now if you multiply each element of one column which two each from other two columns, you will get numbers which are not divisible by 6 but which are dividing 264,600.
For example 1*1*1, 1*1*7, 1*5*7…….and so on.
So total number of all such numbers is product of number of elements in each column which is 7*3*3 = 63

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

goyalsau · Answer

Rahul@gurome wrote:Solution:
264600 = (2^3) * (3^3) * (5^2) * (7^2).

Now we need only those factors that don’t have powers of both 2 and 3 in them because they will combine to give 6. But these factors can contain either only powers of 2 or only powers of 3.

See the table:
1------------1---------1
2------------5---------7
(2^2)------(5^2)----(7^2)
(2^3)
3
(3^2)
(3^3)

Now if you multiply each element of one column which two each from other two columns, you will get numbers which are not divisible by 6 but which are dividing 264,600.
For example 1*1*1, 1*1*7, 1*5*7…….and so on.
So total number of all such numbers is product of number of elements in each column which is 7*3*3 = 63

I am sorry Rahul, I am just not able to understand.
May be i am too dumb.

But now i know that answer is 63
So what i did that total number of factors of 264600 is 144
7^2,5^2,2^3,3^3

3 * 3 * 4 * 4 = 144

then the required answer is 63 means there be 81 factors which will make 6.
I not able to figure out How?

I this can be one way to solve this problem. ( I hope it may be )
if it is then please put some light on it.

gmatmachoman · Answer

Rahul, I am unable to get hold of ur explanation. Plz do write more abt it!! Thx.

Rahul@gurome · Answer

I think there must be a problem in understanding the table.
Column 1 is (1, 2, 2^2, 2^3, 3, 3^2, 3^3)
Column 2 is (1, 5, 5^2)
Column 3 is (1, 7, 7^2).

When you multiply each number of one column with each of other 2 the possible combinations are 1*1*1, 1*1*7, 1*1*(7^2), 1*5*1, 1*5*7….3*1*1, 3*5*7…(3^3)*(5^2)*(7^2). The numbers are then, 1, 7, 49, 5, 35.....and so on and they are all factors of 264600.

Note that the above numbers can have 2,2^2, 2^3, 3,3^2 or 3^3 as factors but they will never have a 2 along with 3. You will not get something like 2*3*5 or (2^2)*3*5from the table.

This means we are eliminating any number which can be divisible by 6.
Hope it is clearer!

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

goyalsau · Answer

Rahul Can't be do it in some simple way.
Like this.
I don't know whether it is possible or not But i think it will be easy to understand.

But now i know that answer is 63
So what i did that total number of factors of 264600 is 144
7^2,5^2,2^3,3^3

3 * 3 * 4 * 4 = 144

then the required answer is 63 means there be 81 factors which will make 6.
I not able to figure out How?

I this can be one way to solve this problem. ( I hope it may be )
if it is then please put some light on it.

Saurabh Goyal
[email protected]
-------------------------

EveryBody Wants to Win But Nobody wants to prepare for Win.

sanju09 · Answer

goyalsau wrote:what to do in this problem?

Lets breakdown the number.

264600=2646*100
=1323*2*5*5*2*2
=441*3*.....
=21*21*3*....
=7*3*7*3*3*2*5*5*2*2
=7^2*3^3*2^3*5 ^2

For a number to be not divisible by 6, it should not be divisible by 3,therefore

Power or 7=2
Power of 3=2
Power of 2=3
Power of 5=2

To get the total number

3*3*4=36

Last edited by sgmuthukumar on Thu Sep 23, 2010 9:42 pm, edited 1 time in total.

goyalsau · Answer

sanju09 wrote:goyalsau wrote:what to do in this problem? 264600 = 2^3 × 3^3 × 5^2 × 7^2, in this, not divisible by 6 are contained in 2^3 × 5^2 × 7^2 and 3^3 × 5^2 × 7^2 only. 2^3 × 5^2 × 7^2 has a total of 4 × 3 × 3 = 36 such divisors and 3^3 × 5^2 × 7^2 has a total of 4 × 3 × 3 = 36 such divisors. In all those 36 + 36 = 72 such divisors, the divisors generated by 5^2 × 7^2, which are 3 × 3 = 9 in number, are included twice; hence we need to subtract 9 from 72 to answer [spoiler]63 as the most appropriate one. D[/spoiler] Great Work Sir I was always sure that you are the one... Thanks.

goyalsau · Answer

sanju09 wrote:goyalsau wrote:what to do in this problem? 264600 = 2^3 × 3^3 × 5^2 × 7^2, in this, not divisible by 6 are contained in 2^3 × 5^2 × 7^2 and 3^3 × 5^2 × 7^2 only. 2^3 × 5^2 × 7^2 has a total of 4 × 3 × 3 = 36 such divisors and 3^3 × 5^2 × 7^2 has a total of 4 × 3 × 3 = 36 such divisors. In all those 36 + 36 = 72 such divisors, the divisors generated by 5^2 × 7^2, which are 3 × 3 = 9 in number, are included twice; hence we need to subtract 9 from 72 to answer [spoiler]63 as the most appropriate one. D[/spoiler] Sanju i was trying to solving differently but I am doing some mistake but not able to get the answer. Brother if can let me know my mistake i will be really helpfull 264600 = 2^3 × 3^3 × 5^2 × 7^2 IN all 4 * 4 * 3 * 3 = 144 factors Now we want 6 out then 2^3 * 3^3 * 5^2 = 4 * 4* 3 = 48 factors and 2^3 * 3^3 * 7^2 = 4 * 4* 3 = 48 factors in all 96 factors common factors 2^3 * 3^3 = 4 * 4 = 16 48 + 48 = 96 - 16 = 80 Now we subtract 144-80 = 64 but the answer is 63 so i want to know which one factor i am missing I know its hard to find problems than doing it all along but i will really thank full if you can let me know my mistake.

sanju09 · Answer

goyalsau wrote:sanju09 wrote:goyalsau wrote:what to do in this problem? 264600 = 2^3 × 3^3 × 5^2 × 7^2, in this, not divisible by 6 are contained in 2^3 × 5^2 × 7^2 and 3^3 × 5^2 × 7^2 only. 2^3 × 5^2 × 7^2 has a total of 4 × 3 × 3 = 36 such divisors and 3^3 × 5^2 × 7^2 has a total of 4 × 3 × 3 = 36 such divisors. In all those 36 + 36 = 72 such divisors, the divisors generated by 5^2 × 7^2, which are 3 × 3 = 9 in number, are included twice; hence we need to subtract 9 from 72 to answer [spoiler]63 as the most appropriate one. D[/spoiler] Sanju i was trying to solving differently but I am doing some mistake but not able to get the answer. Brother if can let me know my mistake i will be really helpfull 264600 = 2^3 × 3^3 × 5^2 × 7^2 IN all 4 * 4 * 3 * 3 = 144 factors Now we want 6 out then 2^3 * 3^3 * 5^2 = 4 * 4* 3 = 48 factors and 2^3 * 3^3 * 7^2 = 4 * 4* 3 = 48 factors in all 96 factors common factors 2^3 * 3^3 = 4 * 4 = 16 48 + 48 = 96 - 16 = 80 Now we subtract 144-80 = 64 but the answer is 63 so i want to know which one factor i am missing I know its hard to find problems than doing it all along but i will really thank full if you can let me know my mistake. You are not trying to answer the central question here, because you are not trying to get the divisors NOT divisible by 6, this way. Because you would not have included "2^3 X 3^3" to factor considerations if you really wanted 6 OUT. Address a different problem, get a different result, no marvel!

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