Real numbers - Fundamental theorem of arithmetic real number for class 10th maths.
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The document discusses the decimal expansion of rational numbers, Euclid's division algorithm, and the fundamental theorem of arithmetic. It provides a solution for finding the highest common factor (HCF) and least common multiple (LCM) of the numbers 16 and 36 using prime factorization. The process involves identifying common and uncommon prime factors to calculate HCF and LCM based on their exponents.
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Real numbers - Fundamental theorem of arithmetic real number for class 10th maths.
- 1. Decimal Expansion Of Rational numbers Euclid’s Division Algorithm Fundamental Theorem Of Arithmetic Proofs Based On Irrational Numbers
- 2. Chapter : Real Numbers Website: www.letstute.com
- 3. Q)Find the HCF and LCM of 16 and 36 by Prime factorisation method. SOLUTION: 16 = 2 × 2 × 2 × 2 = 24 Using the factor tree for prime factorisation, we get Chapter : Real Numbers Website: www.letstute.com Fundamental TheoremOf Arithmetic 36 = 2 × 2 × 3 × 3 = 22 × 32
- 4. Common prime factor 2 HCF = 22 = 4 Common prime factor 2 3 LCM = 𝟐 𝟒 × 𝟑 𝟐 = 16 × 9 = 144 Chapter : Real Numbers Website: www.letstute.com Fundamental Theorem Of Arithmetic 2 Least exponent Greatest exponent 4 2 Uncommon prime factor Greatest exponent
- 5. FACTORIZE THE GIVEN NUMBERS. TO FIND HCF: COLLECT THE COMMON PRIME FACTORS WITH THE LEAST EXPONENT. TO FIND LCM: COLLECT THE COMMON AND UNCOMMON PRIME FACTORS WITH THE GREATEST EXPONENT.