How many ordered pairs of positive integers , satisfy the equation below?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
6 M = N 6
is a ratio ; therefore, we can cross multiply ,
M N = 3 6
Now, we find all the factors of 36,
1 × 3 6 = 3 6 2 × 1 8 = 3 6 3 × 1 2 = 3 6 4 × 9 = 3 6 6 × 6 = 3 6
Now we can reverse the order of the factors for all of the ones listed above, because they are ordered pairs except 6 × 6 since it is the same back if we reverse the order.
4 × 2 + 1 = 9