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