Select the correct alternative from the given choices. The least number, which when successively

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Select the correct alternative from the given choices. The...

Key Concepts

Successive Division Process

Successive division is a method where a number is divided by a divisor and the quotient is further divided by another divisor, and so on. The remainders obtained at each step provide constraints that can be used to reconstruct the original number, a process that highlights the layered structure of division and remainders in number theory.

Division Algorithm

This fundamental concept in number theory states that for any integer dividend and a positive divisor, there exist unique integers (the quotient and the remainder) such that the dividend equals the product of the divisor and the quotient plus the remainder, where the remainder is non-negative and less than the divisor. This forms the basis for understanding remainders in division problems.

Modular Arithmetic

Modular arithmetic involves a system of arithmetic for integers, where numbers “wrap around” after reaching a certain value—the modulus. It is used to represent and solve problems involving remainders and congruences, making it a key tool in analyzing division-based questions.

Back Substitution Method

Back substitution is a technique used to solve problems involving a series of equations derived from successive division. By expressing the original number in terms of the remainders and quotients from each division step and working backward, one can determine the unknown number that satisfies all the given conditions.

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