The Euclidean Algorithm is better for big numbers AND you can program a computer to do it.

This method takes some getting used to!

Let's do another one:

Use the Euclidean Algorithm to find

GCF( 600 , 136 )

 

1 )  600 = __ * 136 + __
What's the most times you can put 136 into 600?  Grab a calculator.

600 / 136 is approximately 4.4

 

600 = 4 * 136 + 56  ...  put 4 in the first blank  ...  what's left over?  600 - 4 x 136


Shift the numbers down...

600 = 4 * 136 + 56  ...  136 = __ * 56 + __  ...  Do it again!

 

The most times 56 goes into 136 ?  Calculator:

136 / 56 is approximately 2.4

 

136 = 2 * 56 + 24  ...  Put 2 in the first blank  ...  The remainder?  136 - 2 x 56 = ?