m7 teorem asas matematik.ppt
DESCRIPTION
M7 Teorem Asas Matematik.pptTRANSCRIPT
-
Minggu 7Wah Mong WehMathematics DepartmentIPGM KSAH
-
The Fundamental Theorem of Arithmetic
Teorem Asas Arithmetik(TAR)
-
The Fundamental Theorem of ArithmeticEvery natural number can be written as the product of primes and (apart from the order in which the primes occur) this factorisation is unique.
-
Teorem Asas ArithmetikTAR memberitahu kita hubungan antara nombor komposit dengan nombor perdana.Teorem ini menyatakan bahawa: Nombor asli boleh difaktorkan secara unik sebagai hasil darab nombor perdana dalam cara yang unik
-
The Fundamental Theorem of Arithmetice.g 60 = 2 x 2 x 3 x 5
60 = 2 x 3 x 2 x 5
60 = 3 x 2 x 2 x 5
-
TAR memberitahu kita bahawa tiada cara untuk memfaktorkan 60 dalam nombor perdana yang lain selain daripada yang ditulis di atas. Pemfaktoran ini adalah unik. Susunan faktor adalah tidak penting
-
Pokok FaktorCara menulis sebarang nombor komposit dalam bentuk hasil darab nombor perdana- Pokok FaktorCari pemfaktoran perdana bagi (a) 60 (b) 380 ( c) 278 dan tulis jawapan dalam bentuk notasi eksponen
-
PRIME NUMBERS
A natural number p is called a prime number if and only if p is greater than 1 and the only natural numbers which are factors of p are 1 and p
-
Nombor PerdanaNombor Perdana adalah integer positif p dimana p>1 jika ia hanya boleh dibahagi oleh nombor positif 1 dan p (diri sendiri)Nombor Perdana adalah nombor yang mempunyai hanya DUA faktor sahaja
-
PRIME NUMBERS
The prime numbers less than 20 are 2,3,5,7,11,13,17, and 19
-
TheoremIf a given prime number p is not a factor of n, then no multiple of p is a factor of n
-
Criterion for finding prime numbersWhether a natural number n is a prime concerns the determination of the largest prime by which we need divide n
-
Example
Is 251 a prime ?
-
Determination of PrimesTo determine whether a natural number n is a prime: Divide n by the successive primes 2, 3, 5, p, where p is the largest prime such that p m and m is given by (m-1)2 < n m2If none of these primes is a factor of n, then n is a prime
-
The sieve of Eratosthenesweek5\The Sieve of Eratosthenes.doc
-
Factor testsTests to decide whether 2 or 5 is a factor of a natural number n( in decimal notation)
-
Factor tests If the units digit is 0,2,4,6, or 8 , then 2 is a factor of n.
If the units digit is 0 or 5, then 5 is a factor of n
-
Factor testsFactor tests can be proved by means of congruence.
-
Conjectures about primesIs there a formula which will yield successive primes ?
-
Conjectures about primes is a prime for n=1 to n =40
is a prime for n=1 to n=79
-
Conjectures about primesTwin primes are two primes whose different is 2. e.g. 11 and 13 Is there an infinite number of primes?
-
Thank You
*