Six recurring nines appear in the decimal places 762 through 767 of π, see Six nines in pi. The digital root of 35967888 is 3 + 5 + 9 + 6 + 7 + 8 + 8 + 8 = 54, 5 + 4 = 9.Ĭasting 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. The digital root of 36 is 3 + 6 = 9, which, as explained above, demonstrates that it is divisible by nine.
The sum of the digits of 41 is 5, and 41 − 5 = 36. The difference between a base-10 positive integer and the sum of its digits is a whole multiple of nine. Another consequence of 9 being 10 − 1, is that it is also a Kaprekar number. In base- N, the divisors of N − 1 have this property. n = 3 is the only other n > 1 such that a number is divisible by n if and only if its digital root is divisible by n. There are other interesting patterns involving multiples of nine: It is often seen with the letter 'G' in the middle, which stands for geometry, a powerful science that helps unravel the mysteries and wonders of nature. Both the square and compasses are architects tools and are used in Masonic ritual as emblems to teach symbolic lessons. That is, if any natural number is multiplied by 9, and the digits of the answer are repeatedly added until it is just one digit, the sum will be nine: In base 10, a positive number is divisible by 9 if and only if its digital root is 9. A group of nine of anything is called an ennead. Since 9 = 3, 9 is an exponential factorial.Ī polygon with nine sides is called a nonagon or enneagon. All subsequent squares of this form are odd. It is the second non-unitary square prime of the form ( p) and the first that is odd. It is the first composite lucky number, along with the first composite odd number and only single-digit composite odd number.ĩ is the only positive perfect power that is one more than another positive perfect power, by Mihăilescu's Theorem.ĩ is the highest single-digit number in the decimal system. It is 3 times 3 and hence the third square number. 
9 is a composite number, its proper divisors being 1 and 3.
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