What number between 1 to 2000 has the factors 1 2 3 4 5 6 7 8 9 and 10?

Answer 1

10=5*2

9= 3*3

8= 2*2*2

7= 7

6= 3*2

5= 5

4= 2*2

3= 3

2= 2

1= 1

We need a product that include all of the combinations in the right column.

Starting from the top:

10 gives us: 5*2

9 gives us: 3*3

8 gives us: 2*2 (we already have the third 2)

7 gives us: 7

6 gives us: nothing (we already have both a 2 and a 3)

5 gives us: nothing

4 gives us: nothing

3 gives us: nothing

2 gives us: nothing

1 gives us: 1 So: 5*2*3*3*2*2*7*1=2520. There is no number between 1 and 2000 that fits.