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Long division of 23,480 / 37 now proceeds as normal yielding 634 with remainder 22. The remainder is multiplied by 3 to get feet and carried up to the feet column. Long division of the feet gives 1 remainder 29 which is then multiplied by twelve to get 348 inches.
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d() is the number of positive divisors of n, including 1 and n itself; σ() is the sum of the positive divisors of n, including 1 and n itselfs() is the sum of the proper divisors of n, including 1 but not n itself; that is, s(n) = σ(n) − n
8 5 (Take the last digit of the number, and check if it is 0 or 5) 8 5 (If it is 5, take the remaining digits, discarding the last) 8 × 2 = 16 (Multiply the result by 2) 16 + 1 = 17 (Add 1 to the result) 85 ÷ 5 = 17 (The result is the same as the original number divided by 5)
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Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.
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