112 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division Concept 2: Divisibility Rules 17. State the divisibility rule for dividing by 2. 18. State the divisibility rule for dividing by 10. 19. State the divisibility rule for dividing by 3. 20. State the divisibility rule for dividing by 5. For Exercises 21–28, determine if the number is divisible by a. 2 b. 3 c. 5 d. 10 (See Example 2.) 21. 45 22. 100 23. 137 24. 241 25. 108 26. 1040 27. 3140 28. 2115 29. Ms. Berglund has 28 students in her class. Can she distribute a package of 84 candies evenly to her students? 30. Mr. Blankenship has 22 students in an algebra class. He has 110 sheets of graph paper. Can he distribute the graph paper evenly among his students? Concept 3: Prime and Composite Numbers For Exercises 31–46, determine whether the number is prime, composite, or neither. (See Example 3.) 31. 7 32. 17 33. 10 34. 21 35. 51 36. 57 37. 23 38. 31 39. 1 40. 0 41. 121 42. 69 43. 19 44. 29 45. 39 46. 49 47. Are there any whole numbers that are 48. True or false? The square of any prime not prime or composite? If so, list them. number is also a prime number. 49. True or false? All odd numbers are prime. 50. True or false? All even numbers are composite. 51. One method for finding prime numbers is the sieve of Eratosthenes. The natural numbers from 2 to 50 are shown in the table. Start at the number 2 (the smallest prime number). Leave the number 2 and cross out every second number after the number 2. This will eliminate all numbers that are multiples of 2. Then go back to the beginning of the chart and leave the number 3, but cross out every third number after the number 3 (thus eliminating the multiples of 3). Begin at the next open number and continue this process. The numbers that remain are prime numbers. Use this process to find the prime numbers less than 50. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
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