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# If x is the number of positive integers that will leave no remainder

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Joined: 02 Sep 2009
Posts: 58449
If x is the number of positive integers that will leave no remainder  [#permalink]

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21 Apr 2016, 00:30
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Difficulty:

35% (medium)

Question Stats:

68% (01:39) correct 32% (01:40) wrong based on 218 sessions

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If x is the number of positive integers that will leave no remainder when divided into 1,880, what is the value of x?

A. 4
B. 6
C. 8
D. 12
E. 16

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Marshall & McDonough Moderator
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Posts: 1684
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Re: If x is the number of positive integers that will leave no remainder  [#permalink]

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21 Apr 2016, 02:13
number of positive integers that will leave no remainder when divided into 1,880 = Number of factors of 1880

1880 = 2^3 * 5 * 47
Number of factors = 4 * 2 * 2 = 16

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Posts: 1873
Re: If x is the number of positive integers that will leave no remainder  [#permalink]

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21 Apr 2016, 02:47
1
Bunuel wrote:
If x is the number of positive integers that will leave no remainder when divided into 1,880, what is the value of x?

A. 4
B. 6
C. 8
D. 12
E. 16

Put simple, we need to find the number of factors of 1,880
We need to break the number in the prime factors form.
1880 = 10*188 = 10*2*94 = 10*2^2*47 = 2^3*5*47

If a number is of the form 2^a*3^b*5^c,
Total factors = (a+1)(b+1)(c+1)

Therefore, number of factors of 1880 = (3+1)(1+1)(1+1) = 16

Correct Option: E
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Re: If x is the number of positive integers that will leave no remainder  [#permalink]

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21 Apr 2016, 08:20
1

To find the number of different factors of a number, we conduct prime factorization, add '1' to each of the powers of primes, and then multiply the powers.

So 1880 = 2^3*5^1*47^1. Hence 4*2*2 = 16 (E)
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If x is the number of positive integers that will leave no remainder  [#permalink]

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22 Apr 2016, 11:30
Bunuel wrote:
If x is the number of positive integers that will leave no remainder when divided into 1,880, what is the value of x?

A. 4
B. 6
C. 8
D. 12
E. 16

This problems test us on the number of prime factors of the number.

$$1880$$= $$2^3$$ x $$5^1$$ x $$47^1$$

Total factors = ( 3+1 ) ( 1 + 1 ) ( 1 + 1 ) = 16

PS : There is nothing important in this problem except understanding the highlighted part, if you get the meaning correctly it will be a 1 minute job
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Re: If x is the number of positive integers that will leave no remainder  [#permalink]

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20 Nov 2018, 06:32
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Re: If x is the number of positive integers that will leave no remainder   [#permalink] 20 Nov 2018, 06:32
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