1. Jim and his study group want to know if 727 is a prime or composite number. H
ID: 3034077 • Letter: 1
Question
1. Jim and his study group want to know if 727 is a prime or composite number. He explained to his group that neither 2, 3, 4, nor 5 were factors of 727 by using divisibility rules. Mary, a member of the group, claimed that they did not have to check 4 since they already knew 2 was not a factor, but Jim disagreed. Jim claimed that it was possible for 4 to be a factor of a number even if 2 was not a factor a. Is Jim's claim correct? Explain. b. the numbers you would check to see ifthey were factors when trying to and determine if 727 is prime composite number. Explain why your list is complete efficient. In other words, explain why you do not need to check any other numbers and explain why you cannot eliminate any numbers from your list. c. Google rules" and write down the rules you understand. Be sure to rewrite the rules in your own words and provide examples to demonstrate how to use each rulesExplanation / Answer
Ans(1.a)
No. Jim's claim is wrong.
because any number that is divisible by 4 is also divisible by 2, They already tested if 727 is not divisible by 2 so there is no way that 727 is going to be divisible by 4.
Ans(1.b)
i will check with all prime numbers that are less than half of 727. I took prime numbers because there won't be any predecesors of that number which can divide 727.
i took till half of 727 only because bigger than half number won't be able to divide even once.
my list is:
2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | 83 | 89 | 97 | 101 | 103 | 107 | 109 | 113 | 127 | 131 | 137 | 139 | 149 | 151 | 157 | 163 | 167 | 173 | 179 | 181 | 191 | 193 | 197 | 199 | 211 | 223 | 227 | 229 | 233 | 239 | 241 | 251 | 257 | 263 | 269 | 271 | 277 | 281 | 283 | 293 | 307 | 311 | 313 | 317 | 331 | 337 | 347 | 349 | 353 | 359
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you can yourself write divisibility rules by searching from internet so i'm not going to write that.
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