Thread: Finding the greatest common divisor

Find the greatest common divisor of a and b for the following and express it in the form am+bn

1) a = 1020 and b = 354
2) a = 2940 and b = 714

Here's what I've got and can someone check the answers:

1) 1020 = (10)(102) = (2)(5)(51)(2) = (2)(5)(17)(3)(2)

352 = (2)(176) = (2)(2)(88) = (2)(2)(2)(2)(2)(11)

Greatest common divisor: (2)(2) = 4

2) 2940 = (10)(294) = (2)(5)(2)(147) = (2)(5)(2)(7)(21) = (2)(5)(2)(7)(7)(3)

714 = (7)(102) =(7)(51)(2) = (7)(17)(3)(2)

Greatest common divisor: (7)(3)(2) = 42

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Is that all that needs to be done? I'm not sure what it means by "express it in the form am+bn".

1. You were asked to find gcd(1020, 354) but you have calculated gcd(1020, 352).

2. Correct.