what is the greatest common factor of 1134218 and 1135620

Heureka's method is from Euclid.....

It says that, if a - b = c  and c / b, then c / a   and c is the greatest common factor of a and b

So

   1135620

 - 1134218

-------------

        1420 

And 1420 / 1134218  →    so,  1420 / 1135620     and is the greatest common factor of both numbers......

Since both 1 134 218 and 1 135 620 are both even, 2 divides into both

1 134 218 ÷ 2 = 567 109

1 134 620 ÷ 2 = 567 810

After going online and finding a list of prime numbers, trying them one by one, you can get to 701:

567 109 ÷ 701 = 809

567 810 ÷ 701 = 810

Since 809 and 810 are relatively prime (no whole number divides into both of them), we can stop.

The greatest common factor is 2 x 701 = 1402.

Actually, I didn't do that. I have a calculator that, if you divide 1134218 by 1135620, you get .9987654321...

Then, by using a button that changes decimal fractions to common fractions, it gives the answer 809/810.

Dividing 1134218 by 809, the result is 1402, which is 701 x 2. Then, I went to an online list of prime numbers and finding 701, I knew that I was finished.

what is the greatest common factor of 1134218 and 1135620

Use the euklid algorithmn:

$$a= 1135620 \ and \ b= 1134218 \ and \ a> b\\ \\
\begin{array}{c|c|c|c|c|c}
\hline
a & b & q & r \\
\hline
1135620 & 1134218 & \frac{a}{b}=\textcolor[rgb]{0,1,0}{1} & \textcolor[rgb]{0,0,1}{1402} & 1135620 = \textcolor[rgb]{0,1,0}{1} * 1134218 + \textcolor[rgb]{0,0,1}{1402} \\
1134218 (old\ b) & 1402(old\ r) & \frac{a}{b}=\textcolor[rgb]{0,1,0}{809} & \textcolor[rgb]{0,0,1}{0} &1134218 = \textcolor[rgb]{0,1,0}{809} * 1134218 + \textcolor[rgb]{0,0,1}{0}& r= 0 \ \textcolor[rgb]{1,0,0}{Stop }\\
\hline
\end{array}$$

if  r = 0 then in the line before r = 1402 is the greatest common factor