How do you find big gcf?

Answer 1

Any gcf can be found by using prime factorization, but I'll show you a different, arguably cooler way to do so. First, I will show you the steps do to it. Below it, I will explain what I did.

gcf (8192, 1296)

=gcf (1296, 416)

=gcf (416, 48)

=gcf (48, 32)

=gcf (32, 16)

=16. WHAT?????

Here's what I did: I divided the bigger number (8192) by the smaller number (1296) and put the remainder (416) in the next row. Now I have the formula (x, y)= (smaller number from row above it, remainder when the two numbers in the row above it are divided). Continue this process until there is no remainder. When there is no remainder, the quotient is the gcf! Here's a check: 8192=2^13

1296=(2^4)(3^4)

They share 2^4=16!

Here's another example:

gcf (1038, 102)

=gcf (102, 18)

=gcf (18, 12)

=gcf (12, 6)

=6.

Check it yourself!

By the way, I am an 11th Grade student in AP Calculus BC who is aspiring to be a mathematician, so I wouldn't risk providing an inaccurate answer!