1. Prime Number: A prime number is any whole number greater than
1 that has exactly two divisors itself and 1. (A number is a divisor
of another number if it divides that number without a remainder.)
Ex: List the prime numbers that are smaller than 20.
1, 3, 5, 7, 11, 13, 17, 19
2. Writing the prime factorization of a number: To write the prime
factorization of a number, write the number as a product of prime
numbers.
Ex: Which of the following represents a prime factorization?
a. 12 = 62
b. 12 = 2^{2} 3
b represents a prime factorization of 12.
You can use a factor tree to find a prime factorization. Express the
given number as the product of two numbers. Then express each
of those as the product of two numbers. Continue this process
until the numbers no longer factoryou will then have the prime
factors.
Note: The following divisibility tests will help you in deciding what
numbers are factors of the given number.
Divisibility test for 2: A given number is divisible by 2 if it ends in
an even digit.
Divisibility test for 3: A given number is divisible by 3 if the sum of
the digits in the number is divisible by 3.
Divisibility test for 5: A given number is divisible by 5 if the last
digit is 5 or 0.
3. Reducing a fraction to lowest terms: A fraction is said to be in lowest terms
if the numerator and denominator have no common
factors other than 1.
To reduce a fraction to lowest terms, divide the numerator and the
denominator by all of the factors that they have in common. If you
do not know the common factors, write the prime factorization of
the numerator and denominator, then divide out the common
factors.
