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28 June, 10:13

Find the gcd of 6, 14, 21 and express it in the form 6r 14s 21t for some integers r, s, and t

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  1. 28 June, 12:33
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    r = 20; s = - 10; t = 1

    Step-by-step explanation:

    The GCD of 6, 14, 21.

    We have to know that gcd (a, b, c) = gcd (gcd (a, b), c)

    Also, gcd (a, b) = au + bv, u & v are integers.

    Now, gcd (6, 14, 21) = gcd (gcd (6, 14), 21)

    = gcd (2, 21)

    = 1

    Again gcd (6, 14) = 2 & gcd (2, 21) = 1

    ⇒ 6 (-2) + 14 (1) = 2 & 2 (-10) + 21 (1) = 1

    Now, gcd (6, 14, 21) = gcd (gcd (6, 14), 21)

    = gcd (2, 21)

    = 2 (-10) + 21 (1)

    = {6 (-2) + 14 (1) } (-10) + 21 (1)

    = 6 (20) + 14 (-10) + 21 (1)

    Therefore, we get: r = 20; s = - 10; t = 1

    Hence, the answer.
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