@TootaHuaDil said:How many numbers less than 100 have exactly 8 divisors? Any short cut for this question?
total 10 numbers?
2*3*5
2*3*7
2*3*11
2*5*7
2*3*13
2^3*3
2^3*5
2^3*11
2^3*7
3^3*2
@bs0409 , @ishu1991 , here is what i thought:-
Let A, B, C ,D represent the birth month of the 4 people.
A,B,C and D can take values from 1-12.
So total cases = 12^4 (the denominator)
Now two of them, lets say C and D, have the same value (either 1,1 or 2,2 or 3,3 etc...)
hence, C & D together can take 12 values (either 1,1 or 2,2 or 3,3 etc...)
A,B can also take 12 values each
the grouping can be done in 4C2 ways.4C2 = 6
therefore, numerator = 12*12*12*6
(12*12*12*6)/(12^4) = 0.5 or 50%
Let A, B, C ,D represent the birth month of the 4 people.
A,B,C and D can take values from 1-12.
So total cases = 12^4 (the denominator)
Now two of them, lets say C and D, have the same value (either 1,1 or 2,2 or 3,3 etc...)
hence, C & D together can take 12 values (either 1,1 or 2,2 or 3,3 etc...)
A,B can also take 12 values each
the grouping can be done in 4C2 ways.4C2 = 6
therefore, numerator = 12*12*12*6
(12*12*12*6)/(12^4) = 0.5 or 50%
@TootaHuaDil said:How many numbers less than 100 have exactly 8 divisors? Any short cut for this question?
No such numbers less than 100 has exactly 8 divisors
@ao4mba
but the qstn is two of them have bdy in same month suppose if both c and d havr bdy in jan they other two cant hve their bdy in jan crct me if i m wrng?
but the qstn is two of them have bdy in same month suppose if both c and d havr bdy in jan they other two cant hve their bdy in jan crct me if i m wrng?
@shattereddream said:No such numbers less than 100 has exactly 8 divisors
24,54,40,56,88, 30,42,66,78,70.
bhai hai na ye sab 8 divisors wale?
bhai hai na ye sab 8 divisors wale?
@TootaHuaDil said:How to solve the question given below by the same method...How many divisors of 21600 are perfect squares?
okay the ans is 12...i did it wrong previously....
here goes the explanation
21600=(2^6)*(3^3)(5^3)
since we need perfect squares lets represent in terms of simple squares of prime nos. and thus we may take...in other words we may chose from........4^3, 9,25.....
=(2^2)^3*(3^2)(5^2)......(last time i don't know why i took...(2^3)^2
...thus it came out to be 16)
total factors----3*2*2
here goes the explanation
21600=(2^6)*(3^3)(5^3)
since we need perfect squares lets represent in terms of simple squares of prime nos. and thus we may take...in other words we may chose from........4^3, 9,25.....
=(2^2)^3*(3^2)(5^2)......(last time i don't know why i took...(2^3)^2
...thus it came out to be 16)total factors----3*2*2
@TootaHuaDil said:How many numbers less than 100 have exactly 8 divisors? Any short cut for this question?
10 numbers
@ishu1991 said:@ao4mbabut the qstn is two of them have bdy in same month suppose if both c and d havr bdy in jan they other two cant hve their bdy in jan crct me if i m wrng?
I think even more than 2 can have their birthday in the same month...the question doesn't say "..only 2 people have birthdays in the same month..."
@adityaknsit said:okay the ans is 12...i did it wrong previously....here goes the explanation21600=(2^6)*(3^3)(5^3)since we need perfect squares lets represent in terms of simple squares of prime nos. and thus we may tak=(2^2)^3*(3^2)(5^2)total factors----3*2*2
21600=(2^6)*(3^3)(5^3)?? bhai ye kaise? :O
@TootaHuaDil said:21600=(2^6)*(3^3)(5^3)?? bhai ye kaise?
my bad......careless mistake.........okay reattempting...
...careless mistake.........okay reattempting...@TootaHuaDil said:21600=(2^6)*(3^3)(5^3)?? bhai ye ka
@TootaHuaDil said:How to solve the question given below by the same method...How many divisors of 21600 are perfect squares?
21600= (2^5)*(3^3)*(5^2)
now the maximum powers to get squares are 4,2,2 respectively
thus
2^4*3^2*5^2
okay
now we have....4^2*9*25
3*2*2=12
picchli baar jaldi mein ek galti ki...us par galat anwer aaya to pehli galti ke upar ek aur galti......and two wrongs make one right karr diya...waise bhi engineers hain, answer pata ho to solution to apne aap hi bana lete hain answer ko suit karrne ke liye......
jokes apart bhai...really sorry....
@TootaHuaDil said:How to solve the question given below by the same method...How many divisors of 21600 are perfect squares?
21600 equal to 2^5*3^3*5^2
we have to take 4^2*9*25
so 3 *2*2 equal to 12 factors
we have to take 4^2*9*25
so 3 *2*2 equal to 12 factors
@TootaHuaDil
Shld be 12..
Given, 21600= 6^3*10^2 = 2^5*3^2*5^2
Thus, Perfect Square factors will be (2^2), (2^4), (3^2), (5^2), (3*2)^2, (3^2*2^4), (3^2*5^2), (5^2*2^2), (5^2*2^4), (3^2*5^2*2^2), (3^2*5^2*2^4) n (1)..
Am nt sure abt 1..Phir bhi hona toh chaiye.. :)
@pyashraj said:@TootaHuaDilShld be 12..Given, 21600= 6^3*10^2 = 2^5*3^2*5^2Thus, Perfect Square factors will be (2^2), (2^4), (3^2), (5^2), (3*2)^2, (3^2*2^4), (3^2*5^2), (5^2*2^2), (5^2*2^4), (3^2*5^2*2^2), (3^2*5^2*2^4) n (1)..Am nt sure abt 1..Phir bhi hona toh chaiye..
sahi hai :)
@TootaHuaDil said:How to solve the question given below by the same method...How many divisors of 21600 are perfect squares?
21600 = 2^5 * 3^3 * 5^2
here from 2 we can consider 3 value. These are 2^0, 2^2, 2^4
from 3 we can consider two vales. These are 3^0, 3^2
from 5 we can consider two vales. These are 5^0, 5^2
Total values = 3 * 2 * 2 = 12