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

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.