Jane was seriously wondering what made her day unhappy and she finally discovered it was the strange answer she gave her little sister on the HCF and LCM calculation. "Anything you multiply by zero is always Zero". she yelled at her little sister. " but how many factors does 9 have?", the little girl cried out. Ehm.... just 3 and 9, Jane said while she was trying to do a snappy check in her head. but her headache was that, if i count forward, i skip with three spaces but if i count backwards with a difference of three spaces i have zero. she shook her head in disagreement. please help Jane out by letting her know if zero is a multiple of 9 or not as she is still in the troubling and disturbing hands of her little sister!
Nice question.
!-=o0o=-!
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All multiples are composite numbers.
Zero is not a composite number, therefore it cannot be a multiple.
0 and 1 have special roles in arithmetic. 0 is the identity element in addition, 1 is the identity element in multiplication.
In multiplication, 0 has its own special property that is derived from the distributive law:
a.(b-b)=a.b - a.b
a.0 = 0
for all a.
Note this is not a one-to-one mapping, therefore there is no inverse and div by 0 is undefined.
Youre right but we should also take it into consideration that when counting the multiples of 3, the first number to be considered is zero because is it also a real number and an addition 3 makes us get the second multiple of 3.