Factorization is used in a variety of mathematical operations, including basic arithmetic, algebra, fractions, and to determine the greatest common factor shared by two numbers. Another type of factorization, prime factorization, is the process of determining which prime numbers to multiply together to get the desired number. Prime numbers are whole numbers greater than one that are evenly divisible only by 1 or itself. Examples of prime numbers include 2, 3, 5, 7, 11, 13, 17 and 23 because they are not evenly divisible by any other number except 1.

A common method of determining factors is the use of a factor tree. Starting with the original number at the top of the page, which in this case is 80, draw two downward-sloping branches. Next, determine two of the known factors of 80, and list one on each branch. For example, if the numbers placed on the first two branches were 2 and 40, a person would then continue to factor by drawing two branches from 40 and providing two factors, such as 5 and 8. Continue to add branches until there are no additional factors remaining. The reason that branches were only drawn on the 40 and not on the 2 is because 2 is a prime factor and cannot be factored any further.

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