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Re: How many factors of 80 are greater than square_root 80? [#permalink]
16 Sep 2010, 06:46

1

This post received KUDOS

Expert's post

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This post was BOOKMARKED

vanidhar wrote:

how many factors of 80 are greater than square_root 80?

a)5

No need to find all factors of 80.

\(\sqrt{80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

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.

Re: How many factors of 80 are greater than square_root 80? [#permalink]
16 Oct 2010, 00:18

8. How many different positive integers are factors of 342? A. 9 B. 11 C. 12 D. 20 E. 22

Bunuel logic gave me only 7 but the andser says 12 .. here the explaination given :

C. From the answers we can see that the list of factors will be relatively small, so it’s easiest just to list them out. The pairs of factors are 1 and 342, 2 and 171, 3 and 114, 6 and 57, 9 and 38, and 18 and 19. That makes 12 factors.

Re: How many factors of 80 are greater than square_root 80? [#permalink]
17 Oct 2010, 04:55

Expert's post

vanidhar wrote:

8. How many different positive integers are factors of 342? A. 9 B. 11 C. 12 D. 20 E. 22

Bunuel logic gave me only 7 but the andser says 12 .. here the explaination given :

C. From the answers we can see that the list of factors will be relatively small, so it’s easiest just to list them out. The pairs of factors are 1 and 342, 2 and 171, 3 and 114, 6 and 57, 9 and 38, and 18 and 19. That makes 12 factors.

It's not MY logic, it's MATH.

According to the formula in my previous post as \(342=2*3^2*19\) then # of factors of 342 equals to \((1+1)(2+1)(1+1)=12\).

Re: How many factors of 80 are greater than square_root 80? [#permalink]
10 Nov 2014, 21:31

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Re: How many factors of 80 are greater than square_root 80? [#permalink]
07 Jan 2015, 08:38

Bunuel wrote:

vanidhar wrote:

how many factors of 80 are greater than square_root 80?

a)5

No need to find all factors of 80.

\(\sqrt{80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

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.

Hope it helps.

Bunuel, Did not get the part where you said root 80 is between 8 and 9..the value of root 80 is 4 root 5..Am i missing something here?

Re: How many factors of 80 are greater than square_root 80? [#permalink]
07 Jan 2015, 08:42

Expert's post

Ralphcuisak wrote:

Bunuel wrote:

vanidhar wrote:

how many factors of 80 are greater than square_root 80?

a)5

No need to find all factors of 80.

\(\sqrt{80}\) is more than 8 and less than 9. So we are asked to find # of factors of 80 which are more than 8.

Now, \(80=16*5=2^4*5\) --> # of factors of 80 is \((4+1)(1+1)=10\) (see below how to find the # of factors of an integer). Out of these 10, following 5 factors are less or equal to 8: 1, 2, 4, 5, and 8. So other 5 factors are more than 8.

Answer: 5.

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.

Hope it helps.

Bunuel, Did not get the part where you said root 80 is between 8 and 9..the value of root 80 is 4 root 5..Am i missing something here?

Thanks in Advance.

\(4\sqrt{5}\approx{8.94}\).

\(\sqrt{81}=9\), thus \(\sqrt{80}\) is a bit less than 9. _________________

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