How do you find the greatest common factor using repeated division?

Answer 1

An example should illustrate the process. Find the common factor of 38 and 14.

Dividing 38 by 14 gives a remainder of 10. Repeat with the smaller two numbers.

14 divide by 10 gives a remainder of 4.

10 divided by 4 gives a remainder of 2.

4 divided by 2 gives a remainder of 0.

The last non-zero number is the greatest common factor. In this case, 2.

Answer 2

The distributive property states that for nonzero values a and b and c, (a+b)/c = a/c + b/c

You can factor some numbers quickly by examining their digits. For example, the number 609 is obviously divisible by 3, because

600 / 3 = 200

9 / 3 = 3

So 609 = 3 x 203

This will not provide all of the prime factors, but it reduces the work required.