Q: Find the HCF of the pair and express it in the form xa + yb = h
966 and 1633
I can find the HCF quite easily. I stuff up when "cleaning up" the equation.
First of all: The final answer to this question is 23 = 22x966-13x1633
My answer is different and here is how I got it:
I got a HCF of 23 and by using the euclidean algorithm. I then showed:
[..]Thus
667 = 1633 - 1x966 [1]
299=966 - 1x667 [2]
69=667 - 2x299 [3]
23=299 - 4x69 [4]
I now tried to express it in the form xa + yb = h
23=299 - 4x69 [from 4]
=299 - 4(667 - 2x299) [from 3]
=
9x299 - 4x667
=
9(966 - 1x667) - 4x667 [from 2]
=
9x966 -
13x667
=
9x966 -
13(1633 - 1x966)
Therefore =
22x966 -
13x1633
Now that is obviously wrong, but I don't know where or how the mistake I made occurred. I hate when I spend ages on a question and it turns out wrong. It lowers my self esteem