A divisor is a number by which another number, called the dividend, is divided. In base systems, divisors play a crucial role in conversion processes and modular arithmetic.
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A divisor of a number divides it exactly without leaving a remainder.
In any integer division, if 'a' is divided by 'b', then 'b' is the divisor.
Divisors are fundamental in understanding prime factorization and greatest common divisors.
In base conversion, divisors are used to repeatedly divide the original number to find its representation in the new base.
The concept of divisors extends to modular arithmetic where numbers are considered equivalent if they have the same remainder when divided by a given divisor.
Review Questions
What is the role of a divisor in integer division?
How does the concept of a divisor apply in converting numbers between bases?
Give an example of how divisors are used in finding the greatest common divisor.