What is number systems, Mathematics

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NUMBER SYSTEMS: Numbers  are intellectual  witnesses  that belong  only  to  mankind.

Example:

If the H C F of 657 and 963 is expressible in the form of 657x + 963x - 15 find x. (Ans:x=22)

Ans:    Using Euclid's Division Lemma a= bq+r , o ≤  r < b

963=657×1+306

657=306×2+45

306=45×6+36

45=36×1+9

36=9×4+0

∴ HCF (657, 963) = 9

now    9 = 657x + 963× (-15)

657x=9+963×15

=9+14445

657x=14454 x=14454/657

x =22


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