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Determine the prime factorization of eac...

Determine the prime factorization of each of the following numbers:    (i) 556920

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AI Generated Solution

To determine the prime factorization of the number 556920, we will follow a systematic approach of dividing the number by the smallest prime numbers until we can no longer divide. Here’s the step-by-step solution: ### Step 1: Check for divisibility by 2 Since 556920 is an even number, it is divisible by 2. \[ 556920 \div 2 = 278460 \] ...
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RD SHARMA-REAL NUMBERS-All Questions
  1. Show that every positive even integer is of the form 2q, and that eve...

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  2. prove that there are infinitely many posititegers.

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

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

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

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

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

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

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

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

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

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

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

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  14. Use Euclid’s division algorithm to find the HCF of 210 and 55.

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  15. If n is a natural number, then 9^(2n)-4^(2n) is always divisible by 5 ...

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  19. A rectangular courtyard is 18m 72cm long and 13m 20cm broad. It is to ...

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  20. If the prime factorization of a natural number n is 2^3*3^2*5^2*6, w...

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