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Math Expert V
Joined: 02 Sep 2009
Posts: 61358
If x is the number of positive integers that will leave no remainder  [#permalink]

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1
9 00:00

Difficulty:   45% (medium)

Question Stats: 64% (01:38) correct 36% (01:43) wrong based on 202 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 D
Joined: 13 Apr 2015
Posts: 1672
Location: India
Re: If x is the number of positive integers that will leave no remainder  [#permalink]

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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

SVP  B
Joined: 06 Nov 2014
Posts: 1867
Re: If x is the number of positive integers that will leave no remainder  [#permalink]

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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
Manager  S
Joined: 23 Jan 2016
Posts: 176
Location: India
GPA: 3.2
Re: If x is the number of positive integers that will leave no remainder  [#permalink]

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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)
Board of Directors D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4842
Location: India
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If x is the number of positive integers that will leave no remainder  [#permalink]

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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

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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_________________ Re: If x is the number of positive integers that will leave no remainder   [#permalink] 02 Jan 2020, 03:28
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