+5265 GCF of 294 and 546
294:1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294.
546:1, 2, 3, 6, 7, 13, 14, 21, 26, 39, 42, 78, 91, 182, 273, 546
42 is the largest factor in both numbers, therefore 42 is the Greatest Common Factor
+2446 We can use the Euclidean algorithm for this:
| \(a=bq+r\) | This is where (a,b) is the number we are trying to find the GCF of. |
| \(546=294q+r\) | How many times can 294 go into 546 without going over? Once! The remainder goes to r. Continue this process until r becomes 0. |
| \(546=\textcolor{blue}{294}*1+\textcolor{red}{252}\) | 294 now becomes your a and 252 becomes your new b. Now, solve again. |
| \(\textcolor{blue}{294}=\textcolor{red}{252}q+r\) | Do the same process. How many times does 252 go into q without going over? Once. The remainder goes to r. |
| \(294=\textcolor{blue}{252}*1+\textcolor{red}{42}\) | |
| \(\textcolor{blue}{252}=\textcolor{red}{42}q+r\) | |
| \(252=\textcolor{blue}{42}*6+\textcolor{red}{0}\) | Now that r=0, look at the r that was immediately previous to, which happens to be 42. This means that the GCF of 294 and 546 is 42. |
