Mathematics

9 is a composite number, its proper divisors being 1 in addition to 3. this is the 3 times 3 and hence the third square number. Nine is a Motzkin number. it is the first composite lucky number, along with the first composite odd number and only single-digit composite odd number.

3 times 3 is one more than 2 times 2 times 2. Thus, 9 is a positive perfect power that is one more than another positive perfect power, and it can be proved by Mihăilescu's Theorem that 9 is the only number having this property.

9 is the highest single-digit number in the decimal system. It is thenon-unitary square prime of the relieve oneself p2 and the first that is odd. any subsequent squares of this defecate are odd.

Since 1, 9 is an exponential factorial.

A polygon with nine sides is called a nonagon or enneagon. A combine of nine of anything is called an ennead.

In base 10, a positive number is divisible by 9 if and only if its digital root is 9. That is, if all natural number is multiplied by 9, and the digits of theare repeatedly added until it is just one digit, the a thing that is caused or presented by something else will be nine:

There are other interesting patterns involving multiples of nine:

This works for all the multiples of 9. is the only other > 1 such(a) that a number is divisible by n whether and only whether its digital root is divisible by n. In base-N, the divisors of − 1 construct this property. Another consequence of 9 being 10 − 1, is that it is also a Kaprekar number.

The difference between a base-10 positive integer and the or done as a reaction to a question of its digits is a whole group of nine. Examples:

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.

Six recurring ninesin the decimal places 762 through 767 of π, see Six nines in pi.

If dividing a number by the amount of 9s corresponding to its number of digits, the number is turned into a repeating decimal. e.g. 274/999 = 0.274274274274...

There are nine Heegner numbers.