Question

1.    Use the Euclidean algorithm to find the greatest common divisor (gcd) of each pairs of integers. Show the steps of calculation.

a) (900,140)                                                                                                         

b) (128,729)

Answer 1

$a:\\900=6\cdot 140+60\\140=2\cdot 60+20\\60=3\cdot 20\\gcd\left( 900,140 \right) =20\\b:\\729=5\cdot 128+89\\128=1\cdot 89+39\\89=2\cdot 39+11\\39=3\cdot 11+6\\11=1\cdot 6+5\\6=1\cdot 5+1\\gcd\left( 128,729 \right) =1$