1. Recently I came across a maths text book where in it was written that 'zero' is a multiple. My thinking is that: if a*b = c then both a and b are factors of c and since zero can never be a factor, neither a nor b can be zero and hence zero can not be a multiple.
   
   
2. Finding the square root by long division;
   
   e.g, sq. root of 144,will be accomplished as fillows:
   
   12_____
   1 | 144
   1
   ___
   22|44
   44
   ----
   
   
   
   1. after the division of the first digit, subsequently two digits are brought down - why?
      
   2. for the second devisor, the 1st quotient is doubled and another appropriate didgit added to accom,plish the division?
      

If there is a mathematical explanation, I would love to know to explain to 7th grade kids.

Thank you.

When you say "a multiple" you probably mean "a composite number".
For me, a multiple is a multiple of something not a stand alone
expression. You are right in that it does not make much sense
to call zero a composite number. It is naturally not a multiple
of anything but itself. Although one may choose not to call it
even that. Whether you do or not is completely inconsequential.

Never in my practice did I miss that algorithm for finding
square roots. Never used it, never will. There's so little
mathematics in it that studying it is a waste of time. There's
so little use for it that wasting time on it is extremely
unwise.

Pairs of numbers and factors of 2 come from the formula

(10a + b)² = 100a² + (2·10·a·b + 1)

Regards,
Alexander Bogomolny