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Numbers and Their Application to Math and Science

Homework for Numbers Lesson 3

  1. What is the sum of the divisors of 24•(25 - 1) and 26•(27 - 1)? Are these numbers perfect?

     

     

  2. For the number 220, find all the factors; add the factors (except itself); count all the factors; find the prime factorization.

     

     

  3. For the number 284, find all the factors; add the factors (except itself); count all the factors; find the prime factorization.

     

     

  4. Extend the Sieve of Erastosthenes to find the prime numbers between 101 and 200.

    101 102 103 104 105 106 107 108 109 110
    111 112 113 114 115 116 117 118 119 120
    121 122 123 124 125 126 127 128 129 130
    131 132 133 134 135 136 137 138 139 140
    141 142 143 144 145 146 147 148 149 150
    151 152 153 154 155 156 157 158 159 160
    161 162 163 164 165 166 167 168 169 170
    171 172 173 174 175 176 177 178 179 180
    181 182 183 184 185 186 187 188 189 190
    191 192 193 194 195 196 197 198 199 200

  5. How large a factorial can you calculate exactly using your calculator?

     

  6. Add the first few odd numbers together. Initially, just the first one. Write it down as sequence member number one. Then the first and second (1 + 3). Write it down as sequence member number two. Then the first three, etc. until you have added the first five together.
    Symbollically this can be expressed as: What pattern is there in the resultant sequence?

  7. Calculate the powers of 11 from 110 up to 116.

     

  8. Prime factor 231 and express it in a form relating it to the triangular number formula.

     

  9. Prime factor 1001.

     

  10. Prime factor 2047 otherwise known as 211 - 1.

     

  11. For both parts, write out the prime factorization. Bonus points for Venn diagram!

    1. Find the GCF(156,182).

       

    2. Find the LCM(496,8128).

       

  12. Find the lowest common multiple and the greatest common factor of:

    1. 60, 72

    2. 12, 20, 36

    3. 9, 12, 14

     

  13. Bob has every sixth night off from work. It happens that tonight has his favorite shows that only come on once a week and he is off to watch them. How long until he gets to watch his shows again?

 

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