Prime Time Practice Answers

Prime Time Practice Answers6. a.51476Factors of 12 Factors of 134231281 131510b. 1 is the only number in the intersectionsince 13 is a prime number.c. Answers will vary; examples includefactors of two different prime numbers(e.g., 5 and 13) or factors of twodifferent relatively prime numbers (e.g.,11 and 14).7. a.25Multiples of 5 Multiples of 25351510203040b. The numbers in the intersection arethe multiples of 10, which is 5 2.Every number that is a multiple of10 must have 5 and 2 as factors since5 2 10.c. 75 would be placed with the multiplesof 5 since it is a multiple of 5 but not amultiple of 2. 90 would be placed in theintersection since it is a multiple ofboth 5 and 2.9112 4 681214 1618 22 2428 32 34 3638268. The fourth number is even. Since the firstthree numbers were even, odd, and odd,respectively, the sum of these three will beeven. Thus, an even number must beadded to this even sum to produce aneven number.Investigation 3 AdditionalPractice1. a. Susan shouldn’t have to wait at all.The #14 bus should arrive at the mallat 10 A.M. and the #11 bus shouldleave the mall for the museum atabout 10 A.M. (since the #11 bus runsevery 12 minutes, it leaves at the top ofevery hour).b. Susan will have to wait 12 minutesbecause the #14 bus should arrive atnoon.c. Both buses are at the mall at 9 A.M.,10 A.M., 11 A.M., and noon because theleast common multiple of 15 and 12 is60.2. a. One rectangle is made with 42 tiles, andthe other is made with 56 tiles.Theseare the only two even multiples of7 between 40 and 60.b. The rectangle with 42 tiles has a lengthof 6, and the rectangle with 56 tiles has alength of 8.These answers are found byfinding the other number in the factorpair with 7 for each rectangle.c. Students’ answers will vary. For 42: 1 42, 2 21, or 3 14. For 56: 1 56, 2 28, or 4 14.3. Jack will only have a conflict one day permonth on the 21 st .The least commonmultiple of 3 and 7 is 21. The nextcommon multiple, 42, is greater than thenumber of days in a month.4. a. Since the numbers are prime, they don’thave any proper factors other than 1.Therefore, their least common multiplewould be their product.© Pearson Education, Inc., publishing as Pearson Prentice Hall. All rights reserved.2