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# If 105 divides into n with no remainder, which of the following must

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If 105 divides into n with no remainder, which of the following must  [#permalink]

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11 Apr 2016, 04:05
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If 105 divides into n with no remainder, which of the following must be a factor of n?

A. 2
B. 4
C. 6
D. 7
E. 11

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Re: If 105 divides into n with no remainder, which of the following must  [#permalink]

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11 Apr 2016, 04:41
If 105 divides into n with no remainder, n must contain one of the factors of 105.
So prime factorization of 105 gives us 5, 3, 7
since 7 is the only factor that appears among the answer choices, D is the right answer.

Hope I am right...
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Re: If 105 divides into n with no remainder, which of the following must  [#permalink]

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11 Apr 2016, 08:31
Bunuel wrote:
If 105 divides into n with no remainder, which of the following must be a factor of n?

A. 2
B. 4
C. 6
D. 7
E. 11

105 divides into n with no remainder.
This means that n is a factor of 105

On factorizing, 105 = 3*5*7
Of the options, Only 7 is a factor of 105
Option D
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Re: If 105 divides into n with no remainder, which of the following must  [#permalink]

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13 Apr 2016, 02:44
105 / n = k (with k an integer)
(7)(5)(3) / n = k

n must have a 7 in his prime factorization to divide 105 without remainder.

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If 105 divides into n with no remainder, which of the following must  [#permalink]

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16 Jun 2016, 14:25
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Top Contributor
Bunuel wrote:
If 105 divides into n with no remainder, which of the following must be a factor of n?

A. 2
B. 4
C. 6
D. 7
E. 11

Another approach is to pick a value for n that satisfies the given condition.
For example, n COULD equal 105

A. 2 is NOT a factor of 105 (ELIMINATE)
B. 4 is NOT a factor of 105 (ELIMINATE)
C. 6 is NOT a factor of 105 (ELIMINATE)
D. 7 IS a factor of 105 (KEEP)
E. 11 is NOT a factor of 105 (ELIMINATE)

Cheers,
Brent
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If 105 divides into n with no remainder, which of the following must  [#permalink]

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30 Jun 2016, 21:40
Bunuel wrote:
If 105 divides into n with no remainder, which of the following must be a factor of n?

A. 2
B. 4
C. 6
D. 7
E. 11

Quote:
Bunuel Sir,

What is the difference between

105 divided into n

AND

105 divided by n

I searched in Google but got more confused.

Here, when you say 105 divides into n, it is written as

n/105

Please correct me if I am wrong.

Regards,
Yosita

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Schools: Boston U '20 (M)
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Re: If 105 divides into n with no remainder, which of the following must  [#permalink]

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18 Oct 2016, 10:19
A cool property => A number is divisible by factors as well as factors of its factors.
e.g => 27 is divisible by 9
here 27 is also divisible by all the factors of 9 => 1,2,9

in the question => 105/n = integer
the number which will be a factor of n must also divide 105
hence the number we choose must also divide 105
only option that divides 105 is D => 7
Hence D .
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Re: If 105 divides into n with no remainder, which of the following must  [#permalink]

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18 Oct 2016, 11:24
N/105 = Some K + 0

N = Some K x 105

N must contain factors of 105

i.e. 5 x 7 x 3

option D
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Re: If 105 divides into n with no remainder, which of the following must  [#permalink]

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15 Mar 2018, 05:31
Bunuel wrote:
If 105 divides into n with no remainder, which of the following must be a factor of n?

A. 2
B. 4
C. 6
D. 7
E. 11

First step : Find prime factors of 105

3 * 5 * 7

Now, 7 must be a factor of n

(D)
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Re: If 105 divides into n with no remainder, which of the following must  [#permalink]

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18 Jun 2018, 08:45
105=3*5*7, from answer choices we see that 7 is option D, which is the correct answer
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Re: If 105 divides into n with no remainder, which of the following must   [#permalink] 18 Jun 2018, 08:45
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