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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

1

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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