What is the continuous division of 36 and 52?

Answer 1

In one application, continuous division can be used to find prime factorizations.

52/2 = 26/2 = 13/13 = 1

36/2 = 18/2 = 9/3 = 3/3 = 1

2 x 2 x 13 = 52

2 x 2 x 3 x 3 = 36

By comparing these factorizations, we can find relationships between the numbers.

Since they have 2 x 2 in common, the GCF of 36 and 52 is 4.

By combining the highest number of each factor (2 x 2 x 3 x 3 x 13), we can find the LCM: 468

We can also use continuous division to find the LCM directly.

2...36...52

2...18...26

3...9...13

3...3...13

13...1...13

......1...1