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Real Numbers - Coggle Diagram
Real Numbers
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Example: To find the Least Common Multiple (L.C.M) of 36 and 56,
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The Fundamental Theorem of Arithmetic states that the prime factorisation for a given number is unique if the arrangement of the prime factors is ignored.
Example: 36=2×2×3×3 OR, 36=2×3×2×3
Therefore, 36 is represented as a product of prime factors (Two 2s and two 3s) ignoring the arrangement of the factors.
To know more about Fundamental Theorem of Arithmetic, visit here.
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To know more about LCM, visit here.
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Given two numbers, we express both of them as products of their respective prime factors. Then, we select the prime factors that are common to both the numbers
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The factor common to 20 and 24 is 2×2, which is 4, which in turn is the H.C.F of 20 and 24.
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If a/b is a rational number, then its decimal expansion would terminate if both of the following conditions are satisfied :
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b) b can be expressed as a prime factorisation of 2 and 5 i.e b=2m×5n where either m or n, or both can = 0.
If the prime factorisation of b contains any number other than 2 or 5, then the decimal expansion of that number will be recurring
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Euclid’s Division Lemma states that given two integers a and b, there exists a unique pair of integers q and r such that a=b×q+r and 0≤r<b.
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In other words, for a given pair of dividend and divisor, the quotient and remainder obtained are going to be unique.
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Euclid’s Division Algorithm is a method used to find the H.C.F of two numbers, say a and b where a> b.
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If r = 0, the H.C.F is b, else, we apply Euclid’s division Lemma to b (the divisor) and r (the remainder) to get another pair of quotient and remainder.
The above method is repeated until a remainder of zero is obtained. The divisor in that step is the H.C.F of the given set of numbers
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The factor common to 20 and 24 is 2×2, which is 4, which in turn is the H.C.F of 20 and 24.
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Given two numbers, we express both of them as products of their respective prime factors. Then, we select the prime factors that are common to both the numbers
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Real numbers are simply the combination of rational and irrational numbers, in the number system. In general, all the arithmetic operations can be performed on these numbers and they can be represented in the number line, also.
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