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# How many factors of 80 are greater than square_root 80?

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How many factors of 80 are greater than square_root 80? [#permalink]  16 Sep 2010, 03:04
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How many factors of 80 are greater than $$\sqrt{80}$$?

A. Ten
B. Eight
C. Six
D. Five
E. Four
[Reveal] Spoiler: OA

Last edited by Bunuel on 11 Nov 2014, 02:33, edited 1 time in total.
Edited the question.
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Re: How many factors of 80 are greater than square_root 80? [#permalink]  16 Sep 2010, 03:28
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vanidhar wrote:
how many factors of 80 are greater than square_root 80?

a)5

The square root condition means you have to find divisors >= 9

So start with 80 and keep dividing till you hit the condition

80 --> can be divided in 2 ways by 2 or by 5 to get (40, 16)

16 --> cant be divided into anything greater than or equal to 9

40 --> can be divided by 2 or by 5 to get (20,8). The 8 doesnt count

20 --> can be divided by 2 or by 5 to get (10,4). The 4 doesnt count

10 --> cant be divided into anything greater than or equal to 9

So we get : 10,20,40,16,80
Hence 5 is answer

It is easier to do this if you make a tree structure on paper ... comes much more naturally
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Re: How many factors of 80 are greater than square_root 80? [#permalink]  16 Sep 2010, 06:46
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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.
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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.
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Re: How many factors of 80 are greater than square_root 80? [#permalink]  16 Oct 2010, 00:21
342 = 2 x 3^2 x 19

Number of factors = (1+1)(2+1)(1+1) = 12

Posted from my mobile device
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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 $$(1+1)(2+1)(1+1)=12$$.

Answer: C.
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Re: How many factors of 80 are greater than square_root 80? [#permalink]  18 Oct 2010, 07:12
apologies for the wording .. My fault .. I did a calculation mistake..
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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?

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