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# What is the smallest integer that can be divided by the product of a

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Math Expert
Joined: 02 Sep 2009
Posts: 54434
What is the smallest integer that can be divided by the product of a  [#permalink]

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16 Aug 2017, 00:21
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Difficulty:

55% (hard)

Question Stats:

63% (01:13) correct 37% (01:10) wrong based on 150 sessions

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What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?

(A) 7

(B) 14

(C) 24

(D) 28

(E) 35

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Joined: 28 May 2017
Posts: 18
Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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16 Aug 2017, 00:28
According to me it is d 28

Coz 7*2=14
Here both 7 and 2 are prime and when their product which is 14 divides 28 quotient is 2
Which is also a prime no

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Joined: 19 Apr 2017
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Concentration: Strategy, Finance
Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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16 Aug 2017, 01:50
1
let the smallest number be n .
n has to be of the form p1*7*p2.
(n/p1*7) would result in p2 . since p1 and 7 cannot be further broken down

a.7 p1=1 ,gives result 1=(not prime) false
b.14 p1=2 ,gives 1 not prime
c.24 not divisible by 7
d.28 => 4x7/2x7 gives 2 => p1 & p2 =2 ,condition holds . correct answer
e.35 p1=5 ,gives 1 (not prime)
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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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17 Aug 2017, 14:15
1
2 is the smallest prime number, so we will use this because we want the smallest possible prime number; 7*2 = 14.

7/14 = Non integer
14/14 = 1 Not prime
24/14 = Non integer
28/14 = 2 Prime number!
35/14 = Non integer
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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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17 Aug 2017, 15:18
We want to find the smallest integer n, where

n/7p = q

and p and q are primes. So

n = 7pq

To make n as small as possible, we want to make the primes p and q as small as possible, so we want p and q to be 2, and n = 28.
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Re: What is the smallest integer that can be divided by the product of a  [#permalink]

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17 Aug 2017, 21:37
s/ 14(7*2) = prime

(A) 7/14 =X
(B) 14/14 =1
(C) 24/14 =X
(D) 28/14 =2
(E) 35/14 = X

Re: What is the smallest integer that can be divided by the product of a   [#permalink] 17 Aug 2017, 21:37
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