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

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Bunuel
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If x is the number of positive integers that will leave no remainder [#permalink] New post   21 Apr 2016, 00:30
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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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OptimusPrepJanielle
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Re: If x is the number of positive integers that will leave no remainder [#permalink] New post   21 Apr 2016, 02:47
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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] New post   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

Answer: E
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Re: If x is the number of positive integers that will leave no remainder [#permalink] New post   21 Apr 2016, 08:20
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Answer would be E.

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] New post   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

Hence answer is 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] New post   27 Jul 2023, 05:12
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Re: If x is the number of positive integers that will leave no remainder [#permalink]
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