Today's soundtrack is Waylon Jennings: Good Hearted Woman.
I'm on to chapter 8, which covers factors and multiples.
Factors: Two factors are multiplied to equal a product. 5 is a factor of 20. If your larger number can divide by the smaller number with no remainder, the smaller number is a factor of the larger number.
Multiples: A multiple is something that is equaled by one factor multiplied by another factor. 20 is a multiple of 5. Every multiple has at least one factor pair. A factor pair is a combination of two numbers that, when multiplied, equal the multiple.
The factor is always smaller than the multiple!
Prime factors are the breakdown of the factor pairs into prime numbers. We use factor trees to break down factor pairs into prime numbers (1, 3, 5, 7, etc).
The Greatest Common Factor of two or more numbers is the largest number that is a factor of both numbers.
Unlike factors, which are a finite set of numbers, multiples are infinite. Multiples of any number are found by multiplying that number by 2, 3, 4, etc.
The Least Common Multiple is the lowest positive number that is a multiple of every number in a set.
I had some difficulty in figuring out how to use the prime number factoring method to determine the LCM; I eventually learned through extra research that if the same prime number shows up the same number of times in multiple factor trees, you just choose that number one time.
