NUMBER CHART PRIMES AND MULTIPLES put a blue dot to the right of each multiple of 3. Circle 5 and put a green dot beneath all multiples of 5. Circle 7 and put a A seventh-grade student, Keith, chose to do a math project red dot to the left of all multiples of 7. Finally, circle all the based on identifying prime numbers with the sieve of remaining numbers which have no colored dots in their Eratosthenes. Keith's innovation to the sieve added extra information. He used a number chart like the one here and squares. put a triangle around 1 because it is neither prime nor com- posite. Then he circled 2 because it was prime and put a black dot above each multiple of 2. Next he moved from 2 to the next undotted number, 3, circled 3 and put a blue dot to the right of each multiple of 3. The chart below has been started using Keith's method. The multiples of 2 have a black dot above them. Circle 3 and 1. How can we be sure that all the circled numbers are prime? 2. How can you use the chart to find all numbers which are multiples of 3 and 5? 3. Keith's chart actually included ull numbers up lo 1000. How many different colors did he use? 11 12 13 i4 15 i6 17 is 19 20 24 25 26 27 20 29 30 34 35 36 37 s 39 do 45 46 47 48 49 55 56 57 58 59 65 66 67 68 69 70 71 72 73 74 75 76 77 i8 79 a0 85 86 87 88 89 90 91 92 93 94 95 96 97 se 99 100 101 102 103 104 105 106 107 108 109 1i0 21 22 23 31 2 33 41 42 43 44 50 51 52 53 54 60 61 62 63 64 81 a2 83 84 111 112 113 114 115 116 117 118 119 120 neither prime nor composite black dot multiple of 2 blue dot multiple of 3 green dot multiple of 5 red dot multiple of 7 prime numbers

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