For how many positive integer x is 130/x an integer?

Question

(A) 8 
(B) 7 
(C) 6 
(D) 5 
(E) 3

BrentGMATPrepNow · Accepted Answer

In order for 130/x to be an integer,  x must be a divisor of 130

So, the question is really asking us to determine the number of positive divisors of 130. 
To do this, we can use the following rule: 
If the  prime factorization  of N = (p^ a )(q^ b )(r^ c ) . . . (where p, q, r, etc are different prime numbers), then N has a total of ( a +1)( b +1)( c +1)(etc) positive divisors.

Example : 14000 = (2^ 4 )(5^ 3 )(7^ 1 )
So, the number of positive divisors of 14000 = ( 4 +1)( 3 +1)( 1 +1) =(5)(4)(2) = 40

Now onto the question.......
130 = (2)(5)(13) = (2^ 1 )(5^ 1 )(13^ 1 )
So, the number of positive divisors of 130 = ( 1 +1)( 1 +1)( 1 +1) =(2)(2)(2) = 8

Answer: A

RELATED VIDEO
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ashudhall · Answer

8 as 130= 13*2*5
 no.of factors = 2*2*2=8
Hence answer should be A

Sent from my ONEPLUS A3003 using  GMAT Club Forum mobile app

BrentGMATPrepNow · Answer

Here are a few similar questions to practice with:

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Cheers,
Brent

Abhishek009 · Answer

The factors of 130 are: 1, 2, 5, 10, 13, 26, 65, 130

So, 130 divided by any of the above 8 numbers will result in an integer..

Thus, answer must be (A) 8

utkarshthapak · Answer

It is a direct question of finding no. of factors.
Factorization of any integer = a^p * b^q * c^r (where a,b,c are prime factors and p,q,r are powers of a,b,c respectively). 
So on factorization of 130, we get 2^1 * 5^1 * 13^1
No. of factors = (p+1)*(q+1)*(r+1) = 2*2*2 = 8.

JeffTargetTestPrep · Answer

If x is a factor of 130, then 130/x is an integer; thus, we need to determine the number of factors that 130 has. 
 
To do so, we can use the rule in which we prime factorize 130, then add 1 to each exponent of each unique prime factor and then multiply those values together.
 
130 = 13 x 10 = 13^1 x 5^1 x 2^1
 
Thus, 130 has (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 total factors.
 
Answer: A

generis · Answer

This question is a version of "find the number of factors." An integer divided by any of its factors equals an integer.

To find the number of factors of 130 (factors 1 and 130 included)**

1) Do the prime factorization of 130:  2^1*5^1*13^1

2) Take the exponents of each prime factor. Add 1 to each.

Exponents are 1, 1, 1 
Add 1 to each, thus: 2, 2, 2

3) Multiply those numbers

2 * 2 * 2 = 8 
There are 8 factors of 130*

Answer A

*Factors of 130 are
1, 2, 5, 10, 13, 26, 65, 130
130 divided by any of them yields an integer

**The theory, from  Bunuel  ,  SEE THIS POST, scroll down to NUMBER OF FACTORS  is,  verbatim

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.

BrentGMATPrepNow · Answer

This question is asking us "How many positive divisors does 130 have?"

We can solve this using genxer123's technique or we can just list the divisors IN PAIRS and then count them. We get:
1 and 130
2 and 65
5 and 26
10 and 13

TOTAL = 8 divisors

Answer:  A

Cheers,
Brent

JeffTargetTestPrep · Answer

If x is a positive integer and 130/x is an integer, then x must be a factor of 130. Thus, we need to determine the number of factors of 130. To determine the number of factors, we break down 130 into its prime factorization, add 1 to the exponent of each unique prime, and then multiply. Thus:

130 = 10 x 13 = 2^1 x 5^1 x 13^1

Thus, 130 has (1 + 1)(1 + 1)(1 + 1) = 2 x 2 x 2 = 8 total factors.

Answer: A

NoviceBoy · Answer

Why don't we include 1 as a value of x. So then the total becomes 9 factors? (If 9 was in the option)

Bunuel · Answer

Actually, 1 is included as a possible value for x in all solutions above. 130 has 8 factors: 1, 2, 5, 10, 13, 26, 65, and 130.

bumpbot · Answer

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For how many positive integer x is 130/x an integer?

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For how many positive integer x is 130/x an integer?

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