If 9 is a common factor, this means 3 is also a common factor.

Because 3 x 3 = 9

So ÷ 9 = ÷ 3 ÷ 3

J, thanks for the comment. You able to get the answer yet?

This question is crazily tough man, what do you think?

It's actually quite doable.


Now we know that 1,2,3 and 9 are factors.

Since the numbers can be divided by both 2 and 3, you can actually multiply the 2 and 3 together. 2 x 3 = 6

So 6 is also a factor. Because ÷ 6 = ÷ 2 ÷ 3

So we have 1,2,3,6,9 as factors.


Let one number be 1 x 2 x 9 = 18

The other number is 5 times this number.

So 5 x 18 = 90

Notice that both numbers can be divided by 18. So 18 is the sixth factor.

You may wonder why we do not multiply
by the 3 and 6 too.

This is so as the factor 3 is already part of the factor 9

(3 x 3 = 9)

The factor 6 is already represented by the factor 2 and 3 (2 x 3 = 6)



Let's say we multiply them by 6 and 3
as well. We will get 1 x 2 x 3 x 6 x 9
= 324

Then the other number = 324 x 5 = 1620.

But the problem now is that both numbers can divided by

1,2,3,4,6,9,12,18,27,36,54,81,108,162,324.

There are now more than 6 common factors, which is not correct as the question states there are exactly 6.

J, thanks for your great effort.