What is the result when the greatest common factor of 6432 and 132 is increased by 11?
To find the greatest common factor of 6432 and 132, I can use the Euclidean algorithm, which repeatedly divides the larger number by the smaller number and replaces it with the remainder, until the remainder is zero. So, I start by dividing 6432 by 132 and get a quotient of 48 and a remainder of 96. Then, I divide 132 by 96 and get a quotient of 1 and a remainder of 36. Next, I divide 96 by 36 and get a quotient of 2 and a remainder of 24. Then, I divide 36 by 24 and get a quotient of 1 and a remainder of 12. Finally, I divide 24 by 12 and get a quotient of 2 and a remainder of 0. Since the remainder is zero, the last divisor, 12, is the greatest common factor of 6432 and 132. To get the result, I need to increase 12 by 11, which gives me 23. 