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# For how many positive integer values of x is 65/x an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 64131
For how many positive integer values of x is 65/x an integer?  [#permalink]

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17 Dec 2018, 00:53
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25% (medium)

Question Stats:

63% (00:46) correct 37% (00:38) wrong based on 94 sessions

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For how many positive integer values of x is $$\frac{65}{x}$$ an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

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Re: For how many positive integer values of x is 65/x an integer?  [#permalink]

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17 Dec 2018, 00:58
1,5,13,65. 4 values.

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Re: For how many positive integer values of x is 65/x an integer?  [#permalink]

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17 Dec 2018, 01:57
Bunuel wrote:
For how many positive integer values of x is $$\frac{65}{x}$$ an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

65= 5^1 * 13^1
factors would be (1+1)* (1+1)= 2*2 = 4 IMO C
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Re: For how many positive integer values of x is 65/x an integer?  [#permalink]

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17 Dec 2018, 02:15
Bunuel wrote:
For how many positive integer values of x is $$\frac{65}{x}$$ an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

To know the number of factors, we must factorize 65.

$$65 = 5^1*13^1$$

Total number of factors : (1 + 1 ) ( 1+ 1) = 4.

.
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Re: For how many positive integer values of x is 65/x an integer?  [#permalink]

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31 Dec 2018, 13:09
I like any questions about finding total number of factors for an integer by using something I learnt from probability.
To find total number of factors for an integer n, we need to factorize the number to product of primes.
Let's use 65 as an example here.
65 = 5 * 13
5 can also be written as: 5^1
13 can also be written as 13^1
Now, how many times you can choose 5? It's can be 5^0 or 5^1
There are two options to pick number 13, 13^0 or 13^1
Since these two events are indepent to each other => total ways to pick the number = 2*2 = 4 => total factors of 65.
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Re: For how many positive integer values of x is 65/x an integer?  [#permalink]

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31 Dec 2018, 19:43
Basically the prompt is asking us what are the factors of 65.
Rule : For any number 1 and itself are always a factor.

So 1,65,5,13
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Re: For how many positive integer values of x is 65/x an integer?  [#permalink]

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30 Mar 2020, 18:46
1
Bunuel wrote:
For how many positive integer values of x is $$\frac{65}{x}$$ an integer?

A. 2
B. 3
C. 4
D. 5
E. 6

Square Root of 65 is approximately 8, so we just have to check numbers/factors less than 8 and more than zero.

1*65
5*13
Re: For how many positive integer values of x is 65/x an integer?   [#permalink] 30 Mar 2020, 18:46