Find # Odd Factors of a Number: 1 to N

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In summary, 105 is the total number of divisors of a number a^n1*b^n2*c^n3. This number can be used to find the total number of odd factors between 1 and N.
  • #1
jeedoubts
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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)
 
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  • #2
Hi jeedoubts! :smile:

(try using the X2 and X2 tags just above the Reply box :wink:)
jeedoubts said:
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) ? :smile:
 
  • #3
tiny-tim said:
Hi jeedoubts! :smile:

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


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

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...
 
  • #4
jeedoubts said:
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) :confused:
 
  • #5
tiny-tim said:
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) :confused:


what about parts b,c and d??:confused::confused:
 
  • #6
Can you check the question?

Are you sure it doesn't start with 135 (rather than 105) ?
 
  • #7
tiny-tim said:
Can you check the question?

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

it is 105 i checked it.
 

Related to Find # Odd Factors of a Number: 1 to N

1. What is the purpose of finding the odd factors of a number?

The purpose of finding the odd factors of a number is to determine all the numbers that can divide the given number evenly and have a remainder of 1. This can be useful in various mathematical applications, such as finding prime numbers or determining the number of divisors a number has.

2. How do you find the odd factors of a number?

To find the odd factors of a number, you can use a simple method of checking all the numbers from 1 to the given number and determining if they are odd and can divide the given number evenly. Another method is to use the prime factorization of the number and identify the prime factors that have an exponent of 0 or 1.

3. What is the range of numbers that can be used for finding odd factors?

The range of numbers that can be used for finding odd factors is from 1 to the given number (N). This means that all odd numbers from 1 to N can be potential odd factors of N.

4. Can a number have an odd factor greater than itself?

No, a number cannot have an odd factor greater than itself. This is because the highest odd factor of a number will always be the number itself (since it can only be divided evenly by 1 and itself).

5. What is the significance of finding the odd factors of a number in real-world applications?

Finding the odd factors of a number has various real-world applications in fields such as cryptography, number theory, and computer science. It can be used to determine the factors of large numbers for encryption purposes, identify prime numbers, and optimize algorithms for efficient computation.

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