Given the numbers A= 2^3.5.7^2 and B= 2^5.3.11.find gcd (A B,) . plz suggest ans in step by step explanation​

Question

Given the numbers A= 2^3.5.7^2 and B= 2^5.3.11.find gcd (A B,) . plz suggest ans in step by step explanation​

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Iris 4 weeks 2021-08-18T14:58:48+00:00 1 Answer 0 views 0

Answers ( )

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    2021-08-18T15:00:04+00:00

    Answer:

    GCD = 8

    Step-by-step explanation:

    Given,

    A = 2^{3} X 5 X 7^{2} = 8 X 5 X 49 = 1,960

    B = 2^{5} X 3 X 11 = 1,056

    Formula to keep in mind

    $ GCD(A,B) = \frac{\left| A\cdot B \right|}{LCM(A,B)} $

    You can also do it by factorization as shown below,

    The factors of 1056 are: 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 32, 33, 44, 48, 66, 88, 96, 132, 176, 264, 352, 528, 1056

    The factors of 1960 are: 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 49, 56, 70, 98, 140, 196, 245, 280, 392, 490, 980, 1960

    So GCD = 8

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