# 6-1 Prime Time - Concepts and Explanations

## Order of Operations

The universally agreed upon order for solving math problems. The acronym PEMDAS is used to help remember the order of the steps.

# Example

- Compute any expression with
**parentheses**. - Compute any
**exponent**. - Do all
**multiplication**and**division**in order from left to right. - Do all
**addition**and**subtraction**in order from left to right.

(4 + 6) x 2 = (10) x 2

= 20

## Distributive Property

The Distributive Property shows how a number can be written as two equivalent expressions. A number can be expressed as both a product and a sum. Multiplication is distributed over addition. It can be helpful for understanding the structure of multidigit multiplication.

# Example

## Prime

A number with exactly two factors, 1 and the number itself.

# Example

Examples of primes are 11, 17, 53, and 101. The number 1 is not a prime number, since it has only one factor.

All of the factors of 11 are 1 and 11. All of the factors of 17 are 1 and 17.

## Composite

A whole number with factors other than itself and 1 or a whole number that is not prime.

# Example

Some composite numbers are 6, 12, 20, and 1,001. Each of these numbers has more than two factors.

All of the factors of 6 are 1, 2, 3, 6. All of the factors of 1,001 are 1, 7, 11, 13, 77, 91, 142 and 1001.

## Common Multiples

A multiple that two or more numbers share. The least common multiple (LCM) of 12 and 18 is 36.

# Example

The first few multiples of 5 are 5, 10, 15, 20, 25, 30, *35*, 40, 45, 50, 55, 60, 65, and *70*.

The first few multiples of 7 are 7, 14, 21, 28,* 35*, 42, 49, 56, 63, *70*, 77, 84, and 91.

From these lists you can see that two common multiples of 5 and 7 are 35 and 70. There are more common multiples that can be found.

## Common Factors

A factor that two or more numbers share. The greatest common factor (CGF) of 12 and 18 is 6.

# Example

The number 7 is a common factor of 14 and 35 because 7 is a factor of 14 (14 = 7 x 2) and 7 is a factor of 35 (35 = 7 x 5).

## Prime Factorization

A product of prime numbers, resulting in the desired number. The prime factorization of a number is unique except for the order of the factors. This is the **Fundamental Theorem of Arithmetic**.

# Example

The prime factorization of 360 is 2 x 2 x2 x3 x5.

Although you can switch the order of the factors, every prime product string for 360 will have three 2s, two 3s and one 5.