+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=294∗1+252 | 294 now becomes your a and 252 becomes your new b. Now, solve again. |
| 294=252q+r | Do the same process. How many times does 252 go into q without going over? Once. The remainder goes to r. |
| 294=252∗1+42 | |
| 252=42q+r | |
| 252=42∗6+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. |
