**A little about the number 9:**

Nine is a composite number, its proper divisors being 1 and 3. It is 3 times 3 and hence the third square number. It is the first composite lucky number.

Nine is the highest single-digit number in the decimal system. It is the second non-unitary square prime of the form (p2) and the first that is odd. All subsequent squares of this form are odd.

9 is an exponential factorial.

In base 10 a number is evenly divisible by nine if and only if its digital root is 9.[3] That is, if you multiply nine by any natural number, and repeatedly add the digits of the answer until it is just one digit, you will end up with nine:

2 × 9 = 18 (1 + 8 = 9)

3 × 9 = 27 (2 + 7 = 9)

9 × 9 = 81 (8 + 1 = 9)

121 × 9 = 1089 (1 + 0 + 8 + 9 = 18; 1 + 8 = 9)

234 × 9 = 2106 (2 + 1 + 0 + 6 = 9)

578329 × 9 = 5204961 (5 + 2 + 0 + 4 + 9 + 6 + 1 = 27 (2 + 7 = 9))

482729235601 × 9 = 4344563120409 (4 + 3 + 4 + 4 + 5 + 6 + 3 + 1 + 2 + 0 + 4 + 0 + 9 = 45 (4 + 5 = 9))

The sum of the digits of 41 is 5, and 41-5 = 36. The digital root of 36 is 3+6 = 9, which demonstrates that it is evenly divisible by nine.

The sum of the digits of 35967930 is 3+5+9+6+7+9+3+0 = 42, and 35967930-42 = 35967888. The digital root of 35967888 is 3+5+9+6+7+8+8+8 = 54, 5+4 = 9.

41-14 = 27. The digital root of 27 is 2+7 = 9.

36957930-35967930 = 990000, which is obviously a multiple of nine.

This works regardless of the number of digits that are transposed. For example, the largest transposition of 35967930 is 99765330 (all digits in descending order) and its smallest transposition is 03356799 (all digits in ascending order); subtracting pairs of these numbers produces:

99765330-35967930 = 63797400; 6+3+7+9+7+4+0+0 = 36, 3+6 = 9.

99765330-03356799 = 96408531; 9+6+4+0+8+5+3+1 = 36.

35967930-03356799 = 32611131; 3+2+6+1+1+1+3+1 = 18, 1+8 = 9.

Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers, known as long ago as the 12th Century.[4]

**The Spiritual Meaning of the #9:**

Nine: The spiritual meaning of number Nine bring us to the very height of vibrational frequencies in this number sequence. Nine represents attainment, satisfaction, accomplishment, and our success to achieve an influence in our circumstances. The spiritual meaning of number Nine deals with intellectual power, inventiveness, influence over situations and things. Nine beseeches us to recognize our own internal attributes, and extend these abilities out into the world to make a positive, influential difference.

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