Mathematical Characteristics of Nine
It is the least number that can be expressed as the sum of cubes of first two numbers.
13 + 23 = 9
2. It is the largest one digit number in Hindu- Arabic Number system.
3. Casting Out Nines is the popular method to check the four fundamental operations ( + , _ , x and ÷)
4. If the sum of the digits of a number is the multiple of nine it is divisible by nine.
58527 is divisible by 9 as 5 + 8 + 5 + 2 + 7 = 27 is divisible by 9.
5. If a number from 1 to 8 is divided by 9 the number which is being divided will be repeated infinitely after decimal.
1/9 =0.1111…. 2/9 =0.2222…. 3/9 =0.3333…. 4/9 =0.4444…. 5/9 =0.5555…. 6/9 =0.6666…. 7/9 =0.7777…. 8/9 =0.8888….
6. It is a composite number with its proper divisor being 1 and 3.
7. A polygon with nine sides is called a nonagon.
8. If you multiply any number by 9 the sum of all digits of the product adds to 9. 578329 × 9 = 5204961 and 5 + 2 + 0 + 4 + 9 + 6 + 1 = 27; 2 + 7 = 9
482729235601 × 9 = 4344563120409 and
4 + 3 + 4 + 4 + 5 + 6 + 3 + 1 + 2 + 0 + 4 + 0 + 9 = 45; 4 + 5 = 9
9. The difference between a base 10 positive integer and the sum of its digits is a multiple of nine.
Example:- Let us take the number 768. The sum of its digit is 7 + 6 + 8 = 21. The difference between 768 and 21 is 768 – 21 = 747 which is divisible by 9.
10. Nine is the atomic number of Fluorine.
11. In Geometry, a circle that passes through the nine points of a triangle is known as Nine point circle. These nine points are- the midpoint of each side of triangle, the foot of each altitude and the midpoint of the line segment from each vertex of the triangle to the ortho center. The nine point circle is also known as Euler’s circle or Feuerbach’s circle.
12. The first 9 numbers can be arranged in a magic square so that all rows, columns and both diagonals have the same sum 15.
4 | 9 | 2 |
3 | 5 | 7 |
8 | 1 | 6 |
13. Nine is the maximum number of cubes that one needed to sum to any positive integer.
14. Take any 3 digit number, invert it and subtract the smallest from the larger. The middle digit will always be 9.
542 – 245 = 297
861 – 168 = 693
15. It is the sum of factorials of 3 consecutive numbers.
1! + 2! + 3! = 1 + 2 + 6 = 9
16. It is the fourth composite number. A composite number has more than 2 factors.
9 has the factors 1, 3 and 9.
17. It is the sum of first 3 odd numbers.
1 + 3 + 5 = 9
18. The nine cubes on the size dish stamp make an impossible figure. This arrangement can’t exist in real world. This is a Swedish postal stamp.
19. The following pattern shows the use of 0 to 9 used once.
9 =
97524 / 10836
= 95823 / 10647
= 95742 / 10638
= 75249 /08361
= 58239 / 06471
= 57429 / 06381
20. Let us play an interesting puzzle on multiplying of a number by 9. Multiply -- 10,112,359,550,561,797,752,808,988,764,044,943,820,224,719 by 9 and you will get the result by simply moving the last nine up to the front. Hence the answer is 910,112,359,550,561,797,752,808,988,764,044,943,820,224,71
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