Practice Questions for Test 3

 

1.    If R = red chip and B = black chip, which integer is modeled by RBBRRRRRR?

2.    Let the letters p, q and r represent different primes. Then p2qr3 has 24 different divisors. So would p23.  Use p, q and r to describe all whole numbers having exactly the following number of divisors.

  1. 2
  2. 4
  3. 12
  4. 3

3.   Determine if the following is true or false without perfoming the actual division.

  1. 13 | 2600000000052
  2. 7 | 14,000,000,000,006

4.  Use divisibility tests to answer the following:

  1. A portion of a twenty digit number is shown, where blanks indicate missing digits: 1234567890__ __ __ __ __ __ __ __ __ 
    If it is known that the number is divisible by 11, give two possibilities for the number.
  2. A portion of a ten digit number is shown, where blanks indicate missing digits: 12345__ 1 __ 2 __ 
    If it is known that the number is divisible by 11, give a possibility for the number.

5.    Use a calculator to give a prime factorizarion of 128304. Write your answer as a product of powers of primes. Then determine how many divisors it has.

6.    Is 25001197 a factor of  210011198 ? If so, find k such that  25001197k  =  210011198. If not, explain why not.

7.    Use the definition of divides to show that each of the following is true. (Hint: Find k that satisfies the definition of divides.)

  1. p3q5r  |  p5q13r7s2
  2. 7 | 0
  3. 0 | 0

8.    How many divisors does each of the following have?

  1. 24
  2. 71119162317
  3. 94113

9.   Find the following using the prime factorization method:

  1. GCD(283754, 233972, 2932597)
  2. LCM(3277112, 33115, 537911)

10.   If GDC(a, b) = 23 and LCM(a, b) =  2233 5 and b = 223 5 then what is a?