Month: May 2014

Problem 321 The product of two numbers is 180. The LCM of the two numbers is 60. What is the GCF of the numbers? Explain how you know.   Solution…

Problem 320 Find the  LCM of the numbers 24 and 32 by using a. The listing multiples method. b. The prime factorization method.   Solution a. 24 = 24, 48,…

Problem 319 Use the prime factorization of 48 and the procedure described , how many factors 48 has.   Solution 48 = 24 x 3  , now increase the exponent…

Problem 318 Which of the following numbers are prime, and how do you know? a. 97        b. 51    c. 143  d. 223   Solution   a. Prime. Because It is…

Problem 317 Classify as true or false, and if false, give a counterexample. a. If 3 │ n, then 9 │ n. b. If 10 │ n , then 5…

Problem 316 Describe how to decide if a number is divisible by a. 2.            b.  3.                      c. 4.                        d. 5.                       e. 6.   Solution   a. Only if unit…

Problem 315 When finding the factors of 841, what is the largest factor you would have to rest? What theorem supports this?   Solution According to the factor test theorem…

Problem 314 What is the shortest length of television cable that could be cut into  either a whole number of 18-ft-pieces or a whole number of 30-ft-pieces?   Solution  …

Problem 313 Show that 1,078 and 3,315 are relatively prime.   Solution   1078 = 1,2,7,11,14,22,49,77,154,539,1078 3315 = 1,3,5,13,15,17,39,51,65,85,195,221,255,663,1105,3315 Two integers are relatively prime if they do not have any…

Problem 312 Use a calculator to help you write the prime factorization of 51,051.   Solution 51051= 3 x 7 x 11 x 13 x 17