Lets breakdown the number.goyalsau wrote:what to do in this problem?
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)...sgmuthukumar wrote:Lets breakdown the number.goyalsau wrote:what to do in this problem?
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
I am sorry Rahul, I am just not able to understand.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
goyalsau wrote:what to do in this problem?
Great Work Sirsanju09 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.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]
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.goyalsau wrote:Sanju i was trying to solving differently but I am doing some mistake but not able to get the 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]
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.
