Tematem pracy jest list do kolegi, w którym tłumaczę mu jakieś matematyczne zagadnienie. Bardzo proszę o sprawdzenie ewentualnych błędów
Dear Suzan,
How are you? I hope you're feel better. I know that because of disease you have a problems at uniwersity and I decided to help you with math.
At the last lesson you have a problem to understand Euclid's algorithm, so I will try to explain this subject for you. Euclid's algorithm it's an efficient method for computing the greatest common divisor of two natural numbers(in short - GCD). For example GCD of 18 and 24 is 6 - so, in this case, it's easy to find it.
It's more difficult to do this for numbers larger than a hundred, or a thousand. Then we have to, unfortuantely, to use Euclid's algorithm... There are two versions of this algorithm: subtraction and division. The way with subtraction is based on the fact, that for numbers, which we looking for GCD, we create a pair, where the first one is a number, which is the smallest and the second one is the difference of number larger and smaller. We repeat the action until tha both of numbers will be equal to each other - value of these numbers is the greatest common divisor. For example: we're loking for GCD(1989, 867), so we create a pair: 1122, 867, where 1122=1989-867, and:
876 1122 102 255
1122-876=255 255-102=153
876 255, and 876>225, so: 102 153
255 867 153-102=51
876-255=612 102 51, and 102>51, so:
225 612 51 102
612-255=357 102-51=51
255 357 51 51 - it's GCD(1989, 867).
357-255=102
255 102, and 255>102, so:
The method of sharing is similar to that of the subtraction, but here the second number isn't a difference it's the rest of the division greater by smaller. The algorithm ends when one of the number is equal to zero.The second one is then the greatest common divisor.
I hope that I helped you. Good luck. I'm looking forward to hearing from you.
Best wishes,
Kasia
Dziękuje za jakokolwiek pomoc
Dear Suzan,
How are you? I hope you're feel better. I know that because of disease you have a problems at uniwersity and I decided to help you with math.
At the last lesson you have a problem to understand Euclid's algorithm, so I will try to explain this subject for you. Euclid's algorithm it's an efficient method for computing the greatest common divisor of two natural numbers(in short - GCD). For example GCD of 18 and 24 is 6 - so, in this case, it's easy to find it.
It's more difficult to do this for numbers larger than a hundred, or a thousand. Then we have to, unfortuantely, to use Euclid's algorithm... There are two versions of this algorithm: subtraction and division. The way with subtraction is based on the fact, that for numbers, which we looking for GCD, we create a pair, where the first one is a number, which is the smallest and the second one is the difference of number larger and smaller. We repeat the action until tha both of numbers will be equal to each other - value of these numbers is the greatest common divisor. For example: we're loking for GCD(1989, 867), so we create a pair: 1122, 867, where 1122=1989-867, and:
876 1122 102 255
1122-876=255 255-102=153
876 255, and 876>225, so: 102 153
255 867 153-102=51
876-255=612 102 51, and 102>51, so:
225 612 51 102
612-255=357 102-51=51
255 357 51 51 - it's GCD(1989, 867).
357-255=102
255 102, and 255>102, so:
The method of sharing is similar to that of the subtraction, but here the second number isn't a difference it's the rest of the division greater by smaller. The algorithm ends when one of the number is equal to zero.The second one is then the greatest common divisor.
I hope that I helped you. Good luck. I'm looking forward to hearing from you.
Best wishes,
Kasia
Dziękuje za jakokolwiek pomoc
