Prime numbers and factorization
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This document defines key concepts related to factors and prime numbers of natural numbers. It explains that factors are numbers that divide a number with no remainder, and that prime numbers only have two factors - 1 and itself. Composite numbers have more than two factors. The prime factors of a number are its factors that are prime numbers. Writing a number as the product of its prime factors is called prime factorization.
Prime numbers and factorization
- 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