Posted - 09/09/2009 : 17:46:05 my son has three problems for homework and it says remember the 1st prime numbers. I don't know what he means by that and the problems are 18, 25, and 30. Please help me with explaining the problems to him. HELP!!!!!

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the_hill1962

Posted - 09/10/2009 : 07:40:25 Probably the problems are "prime factorization". In these problems, you check to see which prime numbers go into the number to be factored. Therefore, a list of prime numbers (or memorizing the first ten or so): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29... These are prime numbers because the only numbers that divide evenly into them are 1 and itself. For example, 6 is not a prime number because 6 divides by not only 1 and 6 but also 2 and 3. 7 is prime because only 1 and 7 go into it. 9 is not prime because 3 goes into it. 11 is prime because nothing except 1 and 11 go into it. 14 is not prime because 2 and 7 go into it. Okay, for the first problem "18", check to see which prime number go into it. Check 2, 3. Note that there is no need to go further. You only need to check the primes that are less than the of the number. In this case, 18 = 4.2426.... and the prime number 5 is larger than that so does not need to be checked. 18 2 = 9. So "2" IS a prime factor. 18 3 = 6. So "3" IS a prime factor. It gets a little more difficult than this. You need to see how many times those prime numbers go into 18. To do this, just keep dividing successively: 182=9. 93=3. 33=1. So the prime factorization of 18 is 2^{1}3^{2}. You see, you divided by 3 twice and 2 once. Instead of doing 25 and 30 for you, here is another example: Try 90: You don't need to go past 90. That is, 9.48... So you list of possible primes is 2, 3, 5, 7. 902=45. 455=9. 93=3. 33=1. So the prime factorization of 90 is 2^{1}3^{2}5^{1} Notice that the MathGoodies CD contains a lesson about this: http://www.mathgoodies.com/lessons/toc_vol3.html however it is not one of the free lessons.