Find # Odd Factors of a Number: 1 to N

[jeedoubts]

1. Homework Statement
N has total 105 factors including 1 and N. then find :
a) the total no of odd factors between 1 and N.
b) if the total number of divisors of N which are multiple of 36 are 45.then the total no of odd factors between 1 and N.
c)the number of ways in which N can be resolved into 2 factors which are relatively prime to each other is equal to 4,then the total no of odd factors between 1 and N.
d) if the total number of divisors of N which are multiple of 216 are 48,then the total no of odd factors between 1 and N.

3. The Attempt at a Solution
total number of divisors of a number a^n1*b^n2*c^n3 is equal to (n1+1)(n2+1)(n3+1)

 

[tiny-tim]

Hi jeedoubts!

(try using the X² and X₂ tags just above the Reply box )

N has total 105 factors including 1 and N. then find :
a) the total no of odd factors between 1 and N.
…
total number of divisors of a number a^n1*b^n2*c^n3 is equal to (n1+1)(n2+1)(n3+1)

Well, 105 = 3*5*7, so how does that help you with a) ?

 

[jeedoubts]

Hi jeedoubts!

(try using the X² and X₂ tags just above the Reply box )


Well, 105 = 3*5*7, so how does that help you with a) ?

we can assume N to be a²b⁴c⁶
and if check if either of a or b or c is even or not so in all 4 answers are possible... Ithink in that way please tell if I'm correct...

 

[tiny-tim]

we can assume N to be a²b⁴c⁶
and if check if either of a or b or c is even or not so in all 4 answers are possible... Ithink in that way please tell if I'm correct...

a b and c must be primes, so only one (or zero) of them can be even …

but there doesn't seem to be enough information to answer a)

 

[jeedoubts]

a b and c must be primes, so only one (or zero) of them can be even …

but there doesn't seem to be enough information to answer a)

what about parts b,c and d??

 

[tiny-tim]

Can you check the question?

Are you sure it doesn't start with 135 (rather than 105) ?

 

[jeedoubts]

Can you check the question?

Are you sure it doesn't start with 135 (rather than 105) ?

it is 105 i checked it.