The greatest common factor (GCF) of 518 and 294 is the largest number that divides both 518 and 294 without leaving a remainder. To find the GCF, we can use the Euclidean algorithm, which involves a series of division steps.
First, divide the larger number by the smaller number:
518 ÷ 294 = 1 with a remainder of 224.
Next, divide the previous divisor (294) by the remainder (224):
294 ÷ 224 = 1 with a remainder of 70.
Now, divide the previous remainder (224) by the new remainder (70):
224 ÷ 70 = 3 with a remainder of 14.
Finally, divide the previous remainder (70) by the new remainder (14):
70 ÷ 14 = 5 with a remainder of 0.
When the remainder is 0, the divisor at that step is the GCF. Therefore, the greatest common factor of 518 and 294 is 14.