Hi, .
Please see below a question on my 11 year old daughter's exam paper that we have no idea of the answer.

Find two numbers which when multiplied together make a thousand. neither of the two numbers must use any zeros.

Then, find two numbers which when multiplied together make a million. again neither of the two numbers must use any zeros.

Is there a quick way to do this rather then guess numbers a multiply them?

Thanks
Alvina

2. Originally Posted by dee@landspace.co.uk
Hi, .
Please see below a question on my 11 year old daughter's exam paper that we have no idea of the answer.

Find two numbers which when multiplied together make a thousand. neither of the two numbers must use any zeros.

Then, find two numbers which when multiplied together make a million. again neither of the two numbers must use any zeros.

Is there a quick way to do this rather then guess numbers a multiply them?

Thanks
Alvina
If you look at all the factor of 1000

$\displaystyle 1000 = 2^3 5^3 = 2 \times 2 \times 2 \times 5 \times 5 \times 5$

then pick three and three such that the product of each have no zeros. The same goes for the next problem.

3. Dear dee@landspace.co.uk,

I suppose that we talk about positive integer numbers.
Divide up 1000 into prime numbers:
1000 = 10*10*10 = 2*2*2*5*5*5.
We have to componate two groups so that the two numbers have not any zeros. Zero will appear if the number containts 2 and 5 together. Therefore the one number = 2*2*2 the other = 5*5*5.

4. Thank you very much indeed for solving this question . you made it look really easy. Thanks

Deee