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# Real Numbers, Prime Numbers, and Absolute Value Study Guide: GED Math (page 3)

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Updated on Mar 23, 2011

### Prime and Composite Numbers

A positive integer that is greater than the number 1 is either prime or composite, but not both. A factor is an integer that divides evenly into a number.

• A prime number has only two factors: itself and the number 1.
• Examples: 2, 3, 5, 7, 11, 13, 17, 19, 23,…

• A composite number is a number that has more than two factors.
• Examples: 4, 6, 8, 9, 10, 12, 14, 15, 16,…

• The number 1 is neither prime nor composite.

Prime factorization is the expression of a positive integer as a product of prime numbers. For example, the prime factor of 72 = 2 × 2 × 2 × 3 × 3.

If the same prime factor occurs more than once, it can be written in exponential form. For instance, the prime factorization of 99 is 3 × 3 × 11. It can also be written as 32 × 11. (See Chapter 5 for a discussion of exponents.)

Prime factorization is usually applied to find the greatest common factor (GCF) or the least common multiple (LCM) of two or more integers.

The greatest common factor (GCF) is the greatest factor that divides into two numbers. To find the GCF of two numbers, list the prime factors of each number. Then, multiply together those factors both numbers have in common. If there are no common prime factors, the GCF is 1.

Example

Find the GCF of 18 and 24.

Prime factors of 18: 2 × 3 × 3

Prime factors of 24: 2 × 2 × 2 × 3

There is one 2 and one 3 in common. The GCF is 2 × 3 = 6.

The least common multiple (LCM) is the smallest number that divides two numbers. To find the LCM of two or more whole numbers, make a list of multiples for each whole number. Continue your lists until at least two multiples are common to all lists. Identify the common multiples. The LCM is the smallest of these common multiples.

Example

Find the least common multiple of 4 and 10.

4: 4, 8, 12, 16, 20, 24,…

10: 10, 20, 30, 40,…

The LCM of 4 and 10 is 20.

### Absolute Value

The absolute value of a number or expression is its numerical value without regard to its sign. The absolute value is always positive because it is the distance of a number from zero on a number line. Absolute value is indicated by the symbol | before and after the number or expression.

Example

|–1| = 1

|2 – 4| = |–2| = 2

For order of operations, the absolute value symbol is treated at the same level as parentheses.

Example

5 × |–13 + 3|

First, evaluate the expression inside the absolute value symbol: 5 × |–10|.

Second, evaluate the absolute value: 5 × 10.

Now, perform the multiplication: 5 × 10 = 50.

Practice problems for these concepts can be found at:

Numbers and Operations Practice Problems: GED Math