A positive integer n less than 7000 is such that the H. C. F. of n and 7000 is 14. Total number of p

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30 Mar 2012 Positive integer

A positive integer n less than 7000 is such that the H. C. F. of n and 7000 is 14. Total number of possible values of n are

OPtion

1) 20
3) 50
3) 80
4) 100
5) 120
6) 150
7) 200
8) 250
9) 300
10) none of these

Solution

7000 = 14 * 2^2 * 5^3
it means to get hcf as 14, 2 and 5 multiple of 14 are non possible cases
now 7000/14 = 500
7000/14*2 = 250
7000/14*5 = 100
7000/14*2*5 = 50
so possible values = 500 - 250 - 100 + 50 = 200

Correct Option: 7 Best Solution (3)

Vignesh   12 years AGO

H.C.F of n and 7000 is 14 means, values of n will divisible by 14.

So, for first 5 divisible value of 14, there is 2 possible values of n and 7000 which H.C.F is 14.
(i.e, n= 14 and n=42)

First 5 Divisible value of 14 = 2 possibles of n.
Multiply 100 on both sides,
Therefore,

5 *100 = 2 *100
First 500 divisible value of 14 = 200 possibles of n

Where 500*4 = 7000(N is lesser than 7000)

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sridhar reddy   12 years AGO

70000=7*2*2*2*5*5*5
n=7*2*x
where x is any natural number except 2 & 5
such that (n,7000)=14
7000/14=500 and n

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Datla Kanthi   12 years AGO

1 to 500 numbers multiplied with 14 we get 7000
7000 = 14*2*2*5*5*5
In 1 t0 500
Numbers divisible by 2 are 250
Numbers divisible by 2 & 5 are 100
Only by 5 are 50
possible values of n are = numbers not divisible by either 2 or 5
= 500 -(250+50) = 200 so option 7

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