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The number 525 and 3000 are both divisib...

The number 525 and 3000 are both divisible only 3,5,15,25,75. What is HCF (525, 3000)? Justify your answer.

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To find the Highest Common Factor (HCF) of 525 and 3000, we can use the prime factorization method. Here are the steps to solve the problem: ### Step 1: Prime Factorization of 525 To find the prime factors of 525, we can divide it by the smallest prime numbers. 1. **Divide by 3**: \[ 525 \div 3 = 175 ...
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NCERT EXEMPLAR-REAL NUMBERS-Real Numbers
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  2. A positive integer is the form of 3q+1 q, being a natural number. Can ...

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  3. The number 525 and 3000 are both divisible only 3,5,15,25,75. What is ...

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  4. Explain why 3 xx 5 xx 7 +7 is a composite number.

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  5. Can two number have 18 as their HCF and 380 as their LCM? Give reason

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  6. Without actually performing the long divison, find if (987)/(10500) wi...

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  7. A rational number in its decimal expansion is 327.7081. What can you s...

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  8. Prove that the square of any positive integer is of the form 4q or ...

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  9. Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3...

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  10. Show that the square of any positive integer cannot of the form 5q+2 o...

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  11. Show that the square of any positive integer cannot be of the form 6m+...

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  12. Show that the square of any odd integer is of the form 4m+1, for some ...

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  13. If n is an odd positive integer, show that (n^2-1) is divisible by 8.

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

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  15. Use Euclid division algorithm to find the HCF of 441, 567 and 693.

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  16. Using Euclid's division algorithm, find the largest number that divide...

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  17. Prove that sqrt3+sqrt5 is irrational

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  18. Show that 12^n cannot end with the digits 0 or 5 for any natural numbe...

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  19. In a morning walk, three persons step off together and their steps mea...

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  20. Write the denominator of the rational number 257/5000 in the form 2^m ...

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