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| 4.05.2008 Prime Numbers A number which has exactly two factors. example 2, 3, 5. Composite Numbers A number which has more than two factors. Example 4, 6, 8. 16.05.2008 Is 1 a prime number? No. 1 is neither prime nor composite because it has only 1 factor. Is Every whole/integer no. rational ? Yes, because every whole no. can be written with denominator 1 that is in the form of p/q where p and q are integers and q is not equal to zero. examples 3 = 3/1, - 9 = - 9/1 Is Every rational no. a whole no./integer ? No. 7/5 is a rational number but not a whole no./ integer. 10 Feb 2009 Fundamental Theorem of Arithmatic Every composite number can be expressed as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur. Correct proof of Fundamental Theorem of Arithmatic Correct proof of Fundamental Theorem of Arithmatic was given by Carl Friedrich Gauss. Relation of 2 numbers with their LCM and HCF LCM × HCF = Product of numbers Theorem on Prime numbers and factors Let n be a prime number. If n divides a^2, then n divides a, where a is a positive integer. |