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Class05_M9_notes_Sep_29-Oct_04.pdf - M9 Class 5 notes...

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M9 Class 5 notes1Number TheoryNumber Theory -The branch of mathematics that deals with the properties and relationships ofnumbersBase 10 refers to the numbering system in common use. Take a number like 475, base ten refers to theposition, the 5 is in the one's place, the 7 is in the ten's place and the 4 is in the hundred's place. Eachnumber is 10 times the value to the right of it, hence the term base ten.Example:3217 = (3×103) + (2×102) + (1×101) + (7×100) noting that 100= 1.If a numberNis divided by a divisor d to give a quotient q and a remainder r, thenN=dq+rExample:N=58, d=7,we obtainq=8 and r=258 = 7×8+21. Prime NumberA Prime Number can be divided evenly only by 1, or itself. (In other words, its factors are only 1 oritself)Example 1:13 can only be divided evenly by 1 or 13, so it is a prime number.Example 2:14 can be divided evenly by 1, 2, 7 and 14 so it is a composite number.2. Composite NumberA Composite Number can be divided evenly by numbers other than 1 or itself. (In other words, it hasmore than the two factors of 1 and itself)Example 1:9 can be divided evenly by 1, 3 and 9, so 9 is a composite number.Example 2:7 can only be divided evenly by 1 and 7, so it is not composite. It must be a prime number.3. Beprisque numberAbeprisque numbernis an integer which is either one more than a prime number and one less than aperfect square, or one more than a square and one less than a prime.The only prime beprisque numbers are 2 and 3. For a prime number to be a beprisque number, it has toneighbor another prime number; the only two primes fitting that bill are of course 2 and 3.The only odd beprisque numbers are 1 and 3. For an odd number to be a beprisque number, it has toneighbor an even prime, and since 2 is the only even prime, only 1 and 3 can be beprisque numbers.
M9 Class 5 notes24. FactorsYou can make the same definitions using Factors."Factors" are the numbers you multiply together to get another number.So here is just a different way of saying the same thing from above.When the only factors of a number are 1 and the number, then it is a Prime NumberExamples:3 = 1 × 3(the only factors are 1 and 3)Prime6 = 1 × 6 or 6 = 2 × 3(the factors are 1,2,3 and 6)CompositeExamples from 1 to 14NumberCan be EvenlyDivided ByPrime, orComposite?1(1 is not considered prime or composite)21, 2Prime31, 3Prime41, 2, 4Composite51, 5Prime61, 2, 3, 6Composite71, 7Prime81, 2, 4, 8Composite91, 3, 9Composite101, 2, 5, 10Composite111, 11Prime121, 2, 3, 4, 6, 12Composite131, 13Prime141, 2, 7, 14Composite.........

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Term
Fall
Professor
stevenson
Tags
Prime number, Divisor, numbering system

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