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Re: positive divisors [#permalink]
10 Dec 2010, 11:00
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shrive555 wrote:
How many odd, positive divisors does 540 have?
6 8 12 15 24
Make a prime factorization of a number: 540=2^2*3^3*5 --> get rid of powers of 2 as they give even factors --> you'll have 3^3*5 which has (3+1)(1+1)=8 factors.
Another example: 60=2^2*3*5 it has (2+1)(1+1)(1+1)=12 factors out of which (1+1)(1+1)=4 are odd: 1, 3, 5 and 15 the same # of odd factors as 60/2^2=15 has.
Answer: B.
MUST KNOW FOR GMAT:
Finding the Number of Factors of an Integer
First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.
The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.
Example: Finding the number of all factors of 450: \(450=2^1*3^2*5^2\)
Total number of factors of 450 including 1 and 450 itself is \((1+1)*(2+1)*(2+1)=2*3*3=18\) factors. For more on number properties check: math-number-theory-88376.html _________________
Re: positive divisors [#permalink]
10 Dec 2010, 11:40
1
This post received KUDOS
Expert's post
shrive555 wrote:
Quote:
MUST KNOW FOR GMAT:
Finding the Number of Factors of an Integer
First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.
The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.
i remembered that, but just caught in the term " odd factors " which is cleared now. All right, this was an odd factor case in which we don't have to consider Power of 2. what if we are asked about only even +ve factors. would then we be considering only power of 2 ? for example: 540 = 2^2*3^3*5 ---- =>(2+1) = 3
No. One way will be to count # of all factors and subtract # of odd factors.
540=2^2*3^3*5 has (2+1)(3+1)(1+1)=24 factors out of which 8 are odd, so 24-8=16 are even. _________________
Re: positive divisors [#permalink]
10 Dec 2010, 11:32
Quote:
MUST KNOW FOR GMAT:
Finding the Number of Factors of an Integer
First make prime factorization of an integer \(n=a^p*b^q*c^r\), where \(a\), \(b\), and \(c\) are prime factors of \(n\) and \(p\), \(q\), and \(r\) are their powers.
The number of factors of \(n\) will be expressed by the formula \((p+1)(q+1)(r+1)\). NOTE: this will include 1 and n itself.
i remembered that, but just caught in the term " odd factors " which is cleared now. All right, this was an odd factor case in which we don't have to consider Power of 2. what if we are asked about only even +ve factors. would then we be considering only power of 2 ? for example: 540 = 2^2*3^3*5 ---- =>(2+1) = 3 _________________
Re: How many odd, positive divisors does 540 have? [#permalink]
28 Nov 2013, 10:00
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Re: How many odd, positive divisors does 540 have? [#permalink]
26 Sep 2015, 00:40
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