- 2 Classify Each Of The Following Statements As True Or False Where A And B Are Whole Numbers A If Gcd A B 1 Then A 1 (45.2 KiB) Viewed 28 times
- 2 Classify Each Of The Following Statements As True Or False Where A And B Are Whole Numbers A If Gcd A B 1 Then A 2 (17.07 KiB) Viewed 28 times
2 Classify each of the following statements as true or false where a and b are whole numbers. a. If GCD(a,b) = 1, then a and b cannot both be even. b. If GCD(a,b)=2, then both a and b are even. c. If a and b are even, then GCD(a,b) = 2 ww 2. a. Choose the correct answer below. A. True If GCD(a,b) = 1, then a and b have no common factors other than 1, which implies they do not have a common factor of 2, OB. True. If GCD(a,b) = 1, then either a or b is equal to 1, and thus cannot both be even. OC. False If GCD(a,b)=1, then all factors of a are also factors of b (and vice versa), and thus a and b are either both even or both oc OD. False If GCD(a,b) = 1, then both a and b are prime, and thus a and b can both be even if they are both equal to 2 b. Choose the correct answer below. A. True. If GCD(a b) = 2, then both a and b have a factor of 2, and thus are both even. OB. True If GCD(a b) = 2, then both a and b contain the square of a number, and, since all square numbers are even, both a and b are OC. False If GCD(a b) = 2, then either a is twice b or b is twice a, and this only implies that either a or b is even OD. False, If GCD(a b)=2. then either a or b is equal to 2, but this does not imply that the other number is also even Phance the correct anewar hal
c. Choose the correct answer below OA False If a and b are even, then GCD(a b) will either be half of a or half of b, which in most cases will not be 2 OB. True If a and b are even, then both a and b have a factor of 2 and thus their greatest common divisor is also 2 OC. True If a and b are even then either a is a multiple of b or b is a multiple of a, which implies that GCD(a b) is 2 OD. False Ita and b are even, then both a and b have a factor of 2, but they could have other common factors and have a GCD(a b) that is greater than 2