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If a , b , c are any three integer, and if a divides bc, then implies ac divides bc. To prove or dis[rove the statement.
Since a|bc , we can find a integer k such that bc = ak....(1)
Since ac also divides bc , we canfind an integer n such that bc = acn...(2)
From (1) and (2) we get acn = ak = a(bc/a).
acn = a(bc/a).
acn = ac (b/a).
Therefore if n = b/a is an integer then only if adivides bc, the ac divides bc.
If b/a is not an integer, then ifa divides bc , then ac doenot divide bc.
Example : a = 6, b=12 and c =8 divides bc = 12*8 =96, ac= 6*8 = 48 divides 96. Here a divides 12.
Example: a = 6, b = 8 , c = 12. bc = 96. 6 divides 96. But 6*12= 72 does not divide 96, as a= 6 does not ivide b = 8.
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