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The product of any three consecutive ...

The product of any three consecutive natural numbers is divisible by 6 (True/false).

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Yes, three consecutive integers can be `n(n+1) and (n+2)`
So, one number of these thre must be divisible by 2 and another one must be divisible by 3. Hence, product of number is divisible by 6.
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NCERT EXEMPLAR-REAL NUMBERS-Real Numbers
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  2. The product of two consecutive integers is divisible by 2. Is this sta...

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  3. The product of any three consecutive natural numbers is divisible b...

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  4. Write whether the square of any positive integer can be of the form 3m...

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  5. A positive integer is the form of 3q+1 q, being a natural number. Can ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Prove that sqrt3+sqrt5 is irrational

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