How do you use upside down division to find the greatest common factor of two numbers?

Answer 1

The upside down division method is used to find the prime factorization of the two numbers. One this has been found the greatest common factor is the product of all the primes which are common to both the numbers.

example: gcf(60, 140)

.....2 |60.............2 |140

..........----..................------

.....2 |30................2 |70

..........----.....................-----

.....3 |15................5 |35

..........----.....................-----

........5 |5..................7 |7

............---.......................---

...............1.........................1

→ 60 = 2 × 2 × 3 × 5

→ 140 = 2 × 2 × 5 × 7

Common primes (bold above) are 2, 2, 5

→ gcf(60, 140) = 2 × 2 × 5 = 20.

When I was taught this at school, the upside down division lines made it a bit messy and only the vertical line was used:

.....2|60.................2|140

.....2|30.................2|70

.....3|15.................5|35

.....5|5....................7|7

..........1..........................1