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Chapter 5: Problem 55

Find the greatest common divisor of the numbers. 240 and 285

Short Answer

Expert verified
The greatest common divisor of 240 and 285 is 15.

Step by step solution

01

Setup Euclid's Algorithm

Begin with the two numbers, 240 and 285. According to Euclid's Algorithm, if we subtract the smaller number (240) from the larger number (285), the GCD will be the same. So, compute the difference 285 - 240 = 45.
02

Next Iteration of Euclid's Algorithm

Now use the smaller number from the original pair (240) and the difference (45) for the next iteration. Again subtract the smaller number from the larger one: 240 - 45 = 195.
03

Continue Euclid's Algorithm

Repeat the above step until the difference is 0. That means, subtract again: 195 - 45 = 150, then: 150 - 45 = 105, then: 105 - 45 = 60, then: 60 - 45 = 15, and finally: 45 - 3*15 = 0. The last non-zero remainder in the process is the GCD of our original numbers.
04

Identify the Greatest Common Divisor

The last non-zero remainder is 15, which is then the greatest common divisor of 240 and 285.

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