Rectangular arrays whose dimensions are whole numbers can be used to illustrate the factors of a number. What can be said about the number of rectangular arrays for each of the following types of numbers? Square number: Select: The number always has an odd number of arrays. Composite number: Prime number:
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For example, 4, 9, 16, 25, etc. For a square number, there is only one rectangular array possible, which is a square. Odd number greater than one: For an odd number greater than one, there will be multiple rectangular arrays possible. For example, the number 3 Show more…
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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 $50 .$ $$ \begin{array}{r|r|r|r|r|r|r|r|r|r} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline 11 & 12 & 13 & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\ \hline 21 & 22 & 23 & 24 & 25 & 26 & 27 & 28 & 29 & 30 \\ \hline 31 & 32 & 33 & 34 & 35 & 36 & 37 & 38 & 39 & 40 \\ \hline 41 & 42 & 43 & 44 & 45 & 46 & 47 & 48 & 49 & 50 \\ \hline \end{array} $$
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