Even Numbers: Natural numbers of the form 2n are called even numbers. Odd Numbers: Natural numbers of the form 2n -1 are called odd numbers. Prime Numbers: The natural numbers greater than 1 which are divisible by 1 and the number itself are called prime numbers, Prime numbers have two factors i. Composite Numbers: The natural numbers which are divisible by 1, itself and any other number or numbers are called composite numbers. For example, 4, 6, 8, 9, 10 etc. Note: 1 is neither prime nor a composite number.
Notice this. Example: Find HCF of 56 and 72? Since remainder is zero, divisor 8 is HCF. Fundamental theorem of Arithmetic Every composite number can be expressed as a product of primes, and this expression is unique, apart from the order in which they appear. Step I: Factorize each of the given positive integers and express them as a product of powers of primes in ascending order of magnitude of primes. Remember this! All Natural Numbers are whole numbers. All Whole Numbers are Integers. All Integers are Rational Numbers.
All Rational Numbers are Real Numbers. Steps: Apply lemma to 56 and To prove irrationality of numbers. To determine the nature of the decimal expansion of rational numbers. Algorithm to locate HCF and LCM of two or more positive integers: Step I: Factorize each of the given positive integers and express them as a product of powers of primes in ascending order of magnitude of primes. To prove Irrationality of numbers: The sum or difference of a rational and an irrational number is irrational.
The product or quotient of a non-zero rational number and an irrational number is irrational. RD Sharma Class 12 Solutions. Watch Youtube Videos.
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