We began your exploration of the world of real numbers and encountered irrational numbers. We continue our discussion on real numbers in this chapter.for geometry homework online We begin with two very important properties of positive integers namely the Euclid’s division algorithm and the Fundamental Theorem of Arithmetic.
Euclid’s division algorithm, as the name suggests, has to do with divisibility of integers. Stated simply, it says any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b. Many of you have online statistics problems
probably recognize this as the usual long division process. Although this result is quite
easy to state and understand, it has many applications related to the divisibility properties
of integers. We touch upon a few of them, and use it mainly to compute the HCF of
two positive integers.
The Fundamental Theorem of Arithmetic, on the other hand, has to do something
with multiplication of positive integers. You already know that every composite number
can be expressed as a product of primes in a unique way—this important fact is the
Fundamental Theorem of Arithmetic. Again, while it is a result that is easy to state and
understand, it has online statistics answers some very deep and significant applications in the field of mathematics.
We use the Fundamental Theorem of Arithmetic for two main applications.
Euclid’s division algorithm, as the name suggests, has to do with divisibility of integers. Stated simply, it says any positive integer a can be divided by another positive integer b in such a way that it leaves a remainder r that is smaller than b. Many of you have online statistics problems
probably recognize this as the usual long division process. Although this result is quite
easy to state and understand, it has many applications related to the divisibility properties
of integers. We touch upon a few of them, and use it mainly to compute the HCF of
two positive integers.
The Fundamental Theorem of Arithmetic, on the other hand, has to do something
with multiplication of positive integers. You already know that every composite number
can be expressed as a product of primes in a unique way—this important fact is the
Fundamental Theorem of Arithmetic. Again, while it is a result that is easy to state and
understand, it has online statistics answers some very deep and significant applications in the field of mathematics.
We use the Fundamental Theorem of Arithmetic for two main applications.
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