Partitioning a line segment, AB, into a ratio a/b involves dividing the line segment into a + b equal parts and finding a point that is a equal parts from A and b equal parts from B. When finding a point, P, to partition a line segment, AB, into the ratio a/b, we first find a ratio c = a / (a + b).
The greatest common factor is the largest number that both numbers can be divided by. For example, in #1, 36 and 9 can both be divided by 9 to become 4 and 1.