find the largest number which divides 615 and 963 leaving remainder 6 in each case (euclids division lemma)​

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find the largest number which divides 615 and 963 leaving remainder 6 in each case (euclids division lemma)​

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Autumn 4 weeks 2021-11-02T05:13:26+00:00 2 Answers 0 views 0

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    0
    2021-11-02T05:14:52+00:00

    Step-by-step explanation:

    To find the largest number which divides 615 and 963 leaving remainder 6 in each case.

    We have to find HCF.

    615 = 3*3*29

    963 = 3*11*29

    HCF = 3*29 = 87

    87 is the largest number which divides 615 and 963 leaving remainder 6 in each case.

    0
    2021-11-02T05:14:59+00:00

      \huge\fbox \red{Solution:}

    Firstly, the required numbers which on dividing doesn’t leave any remainder are to be found.

    This is done by subtracting 6 from both the given numbers.

    So, the numbers are 615 – 6 = 609 and 963 – 6 = 957.

    Now, if the HCF of 609 and 957 is found, that will be the required number.

     \fbox \orange{By applying Euclid's division lemma}

    957 = 609 x 1+ 348

    609 = 348 x 1 + 261

    348 = 261 x 1 + 87

    261 = 87 x 3 + 0.

    ⇒ H.C.F. = 87.

      \fbox \blue{Therefore, the required number is 87.}

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