M4maths Previous Puzzles

15 Apr 2010 Possible combination?

A three digit number is equal to the product of its three digits. How many such numbers are possible?

OPtion

1) 0
2) 1
3) 2
4) 3
5) 4
6) 5
7) 6
8) 7
9) 8
10) 9

Solution

According to the given condition

100x + 10y + z = xyz

(100 – yz)x + 10y +z = 0
x = (10y + z) / (yz – 100)
For every integral value of y and z ranging from 0 to 9, x is negative. Hence no such number is possible.

Correct Option: 1 Best Solution (11)

sanjib biswas   14 years AGO

1st any of digit cant be 0 if any of its digit 1 lowest 3digit no 100 and highest no 199 whose digit products is 81 less than100 similarly if any of digit is 2 then its lowest 3 digit no 200 is greater than the products of its highest 3 digit no i.e. 162 similerly for 3,4,5,6,7,8and 9 so its not possible so ans is 0.

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Arneet   14 years AGO

such number is not possible.

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SUDESHNA SEN   14 years AGO

There is no such number, because the highest 3-digit number is 999 and the product of its 3-digits is= 9*9*9=729

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Dr.Dipin Singh   14 years AGO

If xyz is the number, then...
100*x+10*y+z= xyz, .... then

x = (10*y +z)/(yz-100).....

It is clear that 10*y +z will always be +ve and yz is always less than 100. Then yz-100 will be negative and x will be -ve.

which is not possible.

so no such number is possible.

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kewal   14 years AGO

Not possible.

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Ankur Pandey   14 years AGO

no such numbers are possible 'cos multiplication of three digits is always lesser than the three digit number

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Dimple   14 years AGO

If xyz is the number, then
as per given condition ,

100x+10y+z=x*y*z
or
100*x < x*y*z
or
100< y*z

Hence it is clear that
y*z should be more than 100 which is not possible.

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Amar   14 years AGO

If xyz is the number, then

100x+10y+z=x*y*z
means x*y*z < 100x

y*z is more than 100 which is not possible with any 2 single digit numbers..

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S. Singh   14 years AGO

No such number is possible.

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Saranjit Singh   14 years AGO

Not possible to have such number.

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Karthik Pandiyan   14 years AGO

100 =product(1*0*0)=0
999=product(9*9*9)=729

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