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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.
Cuisenaire rods: 5 (yellow) cannot be evenly divided in 2 (red) by any 2 rods of the same color/length, while 6 (dark green) can be evenly divided in 2 by 3 (lime green). In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. [1]
The Forstner bit continues to be manufactured, although it has evolved into a split-ring design. Also, modern Forstner bits normally feature a (non-screw) lead point (AKA "brad point" or "center spur"), unlike Forstner's original, although rim-guided bits are still available from some manufacturers. [2] [better source needed]
Take each digit of the number (371) in reverse order (173), multiplying them successively by the digits 1, 3, 2, 6, 4, 5, repeating with this sequence of multipliers as long as necessary (1, 3, 2, 6, 4, 5, 1, 3, 2, 6, 4, 5, ...), and adding the products (1×1 + 7×3 + 3×2 = 1 + 21 + 6 = 28). The original number is divisible by 7 if and only if ...
i 6 × 2 i × t i, first form 6 × 2 i × t i, second form ----- 0 3.4641016151377543863 3.4641016151377543863 1 3.2153903091734710173 3.2153903091734723496 2 3.1 596599420974940120 3.1 596599420975006733 3 3.14 60862151314012979 3.14 60862151314352708 4 3.14 27145996453136334 3.14 27145996453689225 5 3.141 8730499801259536 3.141 ...
The fractional portion is discarded (5.5 becomes 5). 5 is halved (2.5) and 6 is doubled (12). The fractional portion is discarded (2.5 becomes 2). The figure in the left column (2) is even, so the figure in the right column (12) is discarded. 2 is halved (1) and 12 is doubled (24). All not-scratched-out values are summed: 3 + 6 + 24 = 33.
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Dividing 272 and 8, starting with the hundreds digit, 2 is not divisible by 8. Add 20 and 7 to get 27. The largest number that the divisor of 8 can be multiplied by without exceeding 27 is 3, so it is written under the tens column. Subtracting 24 (the product of 3 and 8) from 27 gives 3 as the remainder.