Understanding the Ukian Algorithm

The video tutorial introduces the Ukian Algorithm, explaining its use in finding the greatest common divisor (GCD) of two numbers. It provides a step-by-step example calculation and a detailed proof of the algorithm's validity. The tutorial also touches on extended concepts and applications, suggesting further study in elementary number theory.

What is the basic formula of the Ukian Algorithm?

• A = B / Q + R

• A = B * Q + R

• A = B + Q * R

• A = Q * B - R

In the Ukian Algorithm, what does the formula A = B * Q + R represent?

• A method to calculate the product of two numbers

• A formula for calculating the average

• A way to find the sum of two numbers

• A representation of division with remainder

What is the first step in applying the Ukian Algorithm to find the GCD of two numbers?

• Multiply the two numbers

• Add the two numbers

• Divide the larger number by the smaller and find the remainder

• Subtract the smaller number from the larger

In the example given, what is the remainder when 2322 is divided by 654?

• 360

• 294

• 66

• 30

What is the GCD of 2322 and 654 as calculated in the example?

• 18

• 24

• 6

• 12

Why is the Ukian Algorithm considered efficient?

• It uses multiplication only

• It requires no calculations

• It reduces the size of numbers quickly

• It uses addition only

What is the key reason the Ukian Algorithm works?

• It adds numbers

• It multiplies numbers

• It uses the properties of division

• It finds the smallest number

What is the claim made about the GCD in the proof of the Ukian Algorithm?

• GCD of A and B is equal to GCD of B and R

• GCD of A and B is always 1

• GCD of A and B is equal to A + B

• GCD of A and B is equal to B - R

What must be true for D to be a common divisor of A and B?

• D divides neither A nor B

• D divides both A and B

• D divides B only

• D divides A only

What is the extended Ukian Algorithm used for?

• Expressing the GCD as a linear combination

• Calculating the product of two numbers

• Finding the difference between two numbers

• Finding the sum of two numbers