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Euclid's Division Lemma

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Euclid's division lemma states that for any two positive integers, say 'a' and 'b', the condition 'a = bq +r', where 0 ≤ r < b always holds true.
Mathematically, we can express this as 'Dividend = (Divisor × Quotient) + Remainder').
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RD SHARMA-REAL NUMBERS-All Questions
  1. Euclid's Division Lemma

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  2. Three sets of English, Hindi and Mathematics books have to be stack...

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  3. In a seminar. the number of participants in Hindi, English and Mathema...

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  4. Find the largest number that will divide 398, 436 and 542 leaving r...

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  5. Find the HCF and LCM of 144, 180 and 192 by prime factorisation method...

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  6. Explain why 7*11*13+13a n d7*6*5*4*3*2*1 are composite numbers.

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  7. Prove that a positive integer n is prime number, if no prime p less th...

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  8. Show that every positive even integer is of the form 2q, and that eve...

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  9. prove that there are infinitely many posititegers.

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  10. Determine the prime factorization of each of the following numbers:   ...

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  11. Express each of the following positive integers as the product of its ...

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  12. If a and b are two odd positive integers such that a > b, then prove t...

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  13. Prove that one of every three consecutive positive integers is divi...

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  14. Show that the square of an odd positive integer is of the form 8q+1, f...

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  15. Prove that the square of any positive integer is of the form 5q ,5q+1,...

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  16. Prove that if xa n dy are odd positive integers, then x^2+y^2 is even ...

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  17. Show that one and only one out of n ,n+2or ,n+4 is divisible by 3, whe...

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  18. Prove that n^2-n divisible by 2 for every positive integer n.

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  19. The remainder when the square of any prime number greater than 3 is ...

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  20. Use Euclid’s division algorithm to find the HCF of 4052 and 12576.

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