2a.  True
b.    False; counterexample: b = 5, a = 2, c = 3;    2 | (5 - 3) but 2 does not divide 5, 2 does not divide 3.
c.    False; counterexample: a = 4, b = 8; GCD(4, 8) = 4.

3a.  Use the Euclidean algorithm to get 167.
b.    Use your answer to part (a) and the equation GCD(a,b)·LCM(a,b)= a·b to get 23,343,093.

4.   The LCM is the product of the two numbers.  We get this by plugging GCD(a, b) = 1 into the equation GCD(a,b)·LCM(a,b) = a·b.

5a.  At 10:30 a.m. since LCM(30,50) = 150 minutes or 2.5 hours after 8:00 a.m..

6a.  Primes less than 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

b.  41 since it is the largest prime that's less than or equal to the square root of 1703, which is about 41.267.

c.  It is composite since 13 | 1703.  In other words, 1703 = (13)(131).

7.  It has 48 whole number divisors.  Use the prime factorization of 7800 = 2³·3·5²·13 to get that there are
(3 + 1)·(1+1)·(2+1)·(1+1) = 4·2·3·2 = 48 factors.

8.  Let x = number of employees originally.  Then 2/7 x = 240 so x = 840 employees originally.
    (Or use proportional reasoning:  2/7 = 240/x.  Solving for x once again gives x = 840.)

9.  Use proportional reasoning:  Let x = pounds of grapes you can buy with $8.00.  Then 6/(3 ²/³) = 8/x.  Solving for x gives
x = 44/9 pounds.

10.  There are infinitely many correct answers.  Here is one:  7/66, 8/66, 9/66, 10/66, 11/66 and in simplified form these are: 7/66, 4/33, 3/22, 5/33, 1/6.

11.

	7	- ½	x-y
additive inverse	-7	½	-x +y
multiplicative inverse	1/7	-2	1/(x-y)

12.  They're dense.   (Or they have multiplicative inverses (all but 0); or they are closed under division (all but division by 0)).

13.  n = -2

14.  355/66

15.  The digit is 8.

16.  Least --> 0.2, 2/9, .23232323...., 4/17 <-- greatest

17.  0.68686868..., 0.85858585..., 1.0303030303...