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State Euclid's division lemma...

State Euclid's division lemma

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What is the use of Euclid's division lemma ?

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

Knowledge Check

  • By applying Euclid's division lemma, 72 and 28 can be expressed as :

    A
    28 = (72 - 16) `xx 2 `
    B
    `72 =(28xx2)+16`
    C
    `72 =(28xx2)-16`
    D
    `16=72-(28+2)`

    • 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.

    Use Euclid's division lemma lo show that the square of any positive integer is either of th.e 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.)

    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 .]

    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].

    17 = 6 xx2 +5 is compared with Euclid's Division lemma a = bq +r then which number is representing the remainder

    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.

    (i) Use Euclid's division algorithm to find the HCF of: 135 and 225 (ii) Use Euclid's division algorithm to find the HCF of: 196 and 38220 (iii) Use Euclid's division algorithm to find the HCF of: 867 and 255,

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