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# Prime numbers and factorization

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1. + Factors of natural numbers 2010-Baghdad
2. + Factor:  A factor of a natural number n is any number that divides nwith zero remainder.  For example, the factors (divisors) of 20 are 1, 2, 4, 5, 10, and 20. The factors of 25 are 1, 5, and 25. The factors of 37 are 1 and 37.
3. + Prime Numbers  A prime number is a natural number that has only two factors, 1 and the number itself.
4. + Composite Numbers  Natural numbers which have more than two factors are called composite numbers.
5. + Prime numbers less than 100
6. + Prime factorization of natural numbers  The prime factors of a number are the factors of the number which are prime.  Example: The factors of 30 are {1, 2, 3, 5, 6, 10, 15, 30}. Therefore, 2, 3, and 5 are the prime factors of 30.
7. + Prime Factorization  Writing a natural number as a product of its prime factors is called the prime factorization of the natural number.  To find prime factors of a natural number, we divide the number by the smallest possible prime factor each time, and stop when the quotient reaches 1.
8. + Example: Lets find prime factors of 180. 180 2 180 ÷ 2 = 90 (divide 180 by 2, quotient is 90) 90 2 90 ÷ 2 = 45(divide 90 by 2, quotient is 45) 45 3 45 ÷ 3 = 15 (divide 45 by 3, quotient is 15) 15 3 15 ÷ 3 = 5 (divide 15 by 3, quotient is 5) 5 5 5 ÷ 5 = 5 (divide 5 by 5, quotient is 1) 1 stop 180 = 2.2.3.3.5