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The Nature Of NumbersThe nature of a number is the qualities that determine its characteristics and help us to say something about that number. The nature is influenced by the sum-of-digits, positions of digits, and many other characteristics. Some of these features are described below.
Odd or EvenOne characteristic of numbers is odd or even. A number which, when divided by 2 and has a remainder, is said to be odd. The last digit will be either 1, 3, 5, 7 or 9.
If there is no remainder, the number is said to be an even number. The last digit will be either 0, 2, 4, 6 or 8.
'Super' EvenBut there is a 'super' even number which is greater than the first root of 2. A number which is beyond 21 may be said to be 'super' even. 64 (26) is more 'super' than 32 (25). In this category will be numbers with :
Position Of DigitsThe position of a digit can determine some characteristic of a number.
Sum of DigitsThe addition of the digits of a number can say a lot about the character of a number. A number the sum of whose digits, at its roots, is equal to 9 is itself divisible by 9.
Example : Take the number 748,334,898. (If you have any difficulties in pronouncing the number go to Say Numbers With Words for some assistance).
The sum of the digits is 54 and 5+4=9.
This means that 748,334,898 has 9 as a factor. Of course, the number has 18 and 3 and 6, for that matter, as a factor as well, because it also ends with 8.
But the number could have been simply divisible by 3 only, for this purpose.
Take the number 748,334,892 - just 69 less than the number above.
The sum of the digits is 48 and 4+8=12 and 1+2=3.
This means that 3 is a factor of 748,334,829 but not 9.
Divisible by 5 qualityIf the last digit is a 5 or a 0 then the number is also divisible by 5. In addition, if the 5 is immediately preceded by a 2 or a 7 then the number is divisible by 25. Also divisible by 25 are numbers ending with 00 or 50.
Not Divisible by 3 qualitySince we can, by the simple addition of digits, say whether the number is divisible by 3 or NOT, then this allows us to utilize the NOT quality.
The sum of digits of a number NOT divisible by 3 will reduce at its lowest terms to 1 or 2. For instance, the sum of the digits of 748,334,839 = 49 = 13 = 4. Divide 4 by 3 and we get a remainder of 1 - a '1' number.
By that measure, 7 is also a '1' number and 5 and 8 are '2' numbers.
Add just 1 to 748,334,839 to make it 748,334,840 = 41 =5. Divide 5 by 3 and we have a remainder of 2 - a '2' number.
The NOT divisible by 3 events affect additions, subtractions, multiplications and divisions of numbers. A knowledge of this can let you quickly determine if you have made an error when performing any of these operations.
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