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Euclids Division Lemma states that for a...

Euclids Division Lemma states that for any two positive integers a and b, there exists unique integers q and r such that `a=bq+r`, where r must satisfy.

A

`O le r lt b`

B

`O lt r le b`

C

`l lt r lt b`

D

`O lt r lt b`

Text Solution

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The correct Answer is:
A, B
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What is the value of any two positive integers a and 'b' HCF (a, b) xx LCM (a, b) ?

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Knowledge Check

  • For any positive integer a and 3, there ex:ist unique integers q and r such that a = 3q + r, where r must satisfy:

    A
    `0 lt= r lt 3`
    B
    `1 lt r lt3`
    C
    `0 lt rlt 3`
    D
    `0 lt r lt=3`

  • Given two integers a and b where a gt b , there exist unequal integers q and r such that b = qa + r where 0 le r lt a .This is known as

    A
    euclid's algorithm
    B
    division algroithm
    C
    archimedian property
    D
    none of these

  • If a and bare any two positive integers then HCF (a, b) xx LCM (a, b) is equal to

    A
    a + b
    B
    a - b
    C
    `axxb`
    D
    `a-:b`

    • Similar Questions

    Explore conceptually related problems

    Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m+1 or 9m+8.

    By Euclid's division lemma, show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m.

    Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m+1 for some integer m. [Hint : Let x be any positive integer then it is of the form 3q, 3q+1 or 3q+2. Now square each of these and show that they can be rewritten in the form 3m or 3m+1].

    Prove that the product of any two consecutive positive integers is divisible by 2.

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