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Factors of natural numbers2010-Baghdad

+Factor:

A factor of a natural number n is any number that divides n with 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.

+Prime Numbers

A prime number is a natural number that has only two factors, 1 and the number itself.

+Composite Numbers

Natural numbers which have more than two factors are called composite numbers.

+Prime numbers less than 100

+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.

+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.

+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)

5 5 5 ÷ 5 = 5 (divide 5 by 5, quotient is 1)

15 3 15 ÷ 3 = 5 (divide 15 by 3, quotient is 5)

45 3 45 ÷ 3 = 15 (divide 45 by 3, quotient is 15)

1 stop 180 = 2.2.3.3.5