+0  
 
0
73
3
avatar

what is the highest common factor of 294 and 546

Guest Sep 21, 2017
Sort: 

3+0 Answers

 #1
avatar+5197 
+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

rarinstraw1195  Sep 21, 2017
 #2
avatar+1221 
+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.
   
TheXSquaredFactor  Sep 21, 2017
 #3
avatar+76929 
+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

 

 

cool cool cool

CPhill  Sep 21, 2017

22 Online Users

avatar
avatar
avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details