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To test for divisibility by D, where D ends in 1, 3, 7, or 9, the following method can be used. [12] Find any multiple of D ending in 9. (If D ends respectively in 1, 3, 7, or 9, then multiply by 9, 3, 7, or 1.) Then add 1 and divide by 10, denoting the result as m.
It seems that if Divisibility Rule is a separate article, then this should not be there. If an integer n is written in base b, and d is an integer with b ≡ 1 (mod d), then n is divisible by d if and only if the sum of its digits is divisible by d. The rules for d=3 and d=9 given above are special cases of this result (b=10).
2.1 Divisibility rule. 2.2 Properties of the number. 2.3 Related properties. 2.4 Numeral systems. ... "If you only knew the magnificence of the 3, 6, and 9, ...
Digit sums and digital roots can be used for quick divisibility tests: a natural number is divisible by 3 or 9 if and only if its digit sum (or digital root) is divisible by 3 or 9, respectively. For divisibility by 9, this test is called the rule of nines and is the basis of the casting out nines technique for checking calculations.
In arithmetic, for example, when multiplying by 9, using the divisibility rule for 9 to verify that the sum of digits of the result is divisible by 9 is a sanity test—it will not catch every multiplication error, but is a quick and simple method to discover many possible errors.
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From January 2008 to December 2012, if you bought shares in companies when Robert A. Profusek joined the board, and sold them when he left, you would have a -51.4 percent return on your investment, compared to a -2.8 percent return from the S&P 500.