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# homework

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what is the highest common factor of 294 and 546

Sep 21, 2017

#1
+5258
+1

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

Sep 21, 2017
#2
+2339
+1

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.
Sep 21, 2017
#3
+96106
+1

Yet...one more way.....!!!!

294  =

2 * 147 =

2 * 3 * 49 =

2 * 3 * 7 * 7

546  =

2 * 273 =

2 * 3 * 91  =

2 * 3 * 7 * 13

Match the factors in red

2 * 3 * 7   =  42

Sep 21, 2017