Propositions  deduced  from  these  principles :

1.  Every  number  ending  with  0,  2,  4,  6,  or  8,  is  divisible  by  2.
2.  Every  number  is  divisible  by  4,  when  the  number  denoted
by  its  two  right  hand  digits  is  divisible  by  4.
3.  Every  number  is  divisible  by  5,  whose  right  hand  digit
is  0  or  5.
4.  Every  number  whose  first  digits  are  0,  00,  &c.,  is  divisible
by  10,  100,  &LC.
The  converse  of  each  of  the  preceding  propositions  is  also  true.
Thus,  no  number  is  divisible  by  2,  unless  it  ends  with  0,  2,  4,  6,
or  8.
5.  Every  composite  number  is  divisible  by  the  product  of  any
two  or  more  of  its  prime  factors.
6.  Every  prime  number,  except  2  or  5,  ends  with  1,  3,  7,  or  9.
Rule  for  resolving  a  composite  number  into  its  prime  fac-
tors. —  Divide  the  given  number  hy  any  prime  number  that  will
exactly  divide  it ;  divide  the  quotient  again  in  the  same  manner^  and
so  continue  to  divide  until  a  quotient  is  obtained  which  is  a  prime
number  ;  then  the  last  quotient  and  the  several  divisors  are  tlw  prime
factors  of  the  given  number.
FACTORING  OF    ALGEBRAIC    aUANTITIES.
Art.  88,  a  divisor ,  or  factor  of  a  quantity,  is  a  quantity  that
will  exactly  divide  it ;  that  is,  without  a  remainder.  Thus,  a  is  a
factor  or  divisor  of  db,  and  a-\-x  is  a  divisor  or  factor  of  a^ — x^.
Art.  89.  A  prime  quantity  is  one  which  is  exactly  divisible
only  by  itself  and  by  unity.  Thus,  a:,  y,  and  x-\-z,  are  prime
quantities  ;  while  xy,  and  ax-\'aZf  are  not  prime.
