1. Find the common factors of two or more numbers2. Determine the greatest common factor (GCF) of

two or more numbers3. Determine whether a number is prime, composite,

or neither.4. Determine the prime factorization of a given

number5. Write the prime factorization using exponents6. Find the common multiples of two or more

numbers7. Determine the least common multiple (LCM) of

two or more numbers.

Composite Number: a number that has more than two factors.Example: 4, 28, 100

Prime Number: a number that only has two factors; one and itself.Example: 5, 29, 101

Primes less than 40:

2 3 5 7 11

13

17

19

23

29

31

37

Two numbers that are neither prime nor composite: 0 and 1 .

Prime Factorization: writing a number as a product of its prime factors.Example: 30 = 2 x 3 x 5

You find the prime factorization of a number by making a factor tree.

STEPS Calculations

1. Break the number down into two of its factors, using a factor tree.

100

20 5

2. Since 5 is a prime number we circle it (this means it is one of the prime factors of 100). 20 is a composite number, we repeat Step 1.

5 4

3. Since 5 is a prime number we circle it. 4 is a composite number, we repeat Step 1.

2 2

4. Since all the numbers are broken into prime factors, we use them to write the product.

2 x 2 x 5 x 5

5. Then we write the prime factorization in exponential form (using exponents). 2² x 5²

Common Factors: factors that two or more numbers have in common.Example: Find all the common factors of 10 and 20 by listing all the factors. 10: 1, 2, 5, 10 20: 1, 2, 4, 5, 10, 20

Greatest Common Factor (GCF): the biggest factor that two numbers have in common.

There are two different ways to find the GCF of two or more numbers.

Using a list: List all the factors of each number. Circle the greatest common factor that appears in the list.12 18

1 12 1 182 6 2 93 4 3 6

Using Prime Factorization: Find the prime factorizations of each number. Circle all the common prime factors. Multiply the common prime factors to get the GCF.12 18

4 3 3 6

2 2 2 3 2² x 3 2 x 3² GCF = 2 x 3 = 6

Museum employees are preparing an exhibit of ancient coins. They have 49 copper coins and 35 silver coins

to arrange on the shelves. Each shelf will have the same number of copper coins and the same number of silver coins. How many shelves

will the employees need for the exhibit?

7 shelves

Multiple: a product of that number and another whole number. Example:

The multiples of 8 - 8, 16, 24, 32, 40 …

Common MultiplesExample: Find some common multiples of

4 and 6 by listing at least ten multiples4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44…6, 12, 18, 24, 30, 36, 42, 48, 53, 60, 66…

• Least Common Multiple: the smallest multiple that two number have in common.

There are two different ways to find the LCM of two or more numbers.

Using a list: List about ten multiples of each number. Circle the lowest common multiple that appears in the list.10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100…

12: 12, 24, 36, 48, 60, 72, 84, 96, 108…

Using Prime Factorization: Find the prime factorizations of each number. Write them in exponential form. Take each number that is used. If they are used more than once, use the one with the biggest exponent. Multiply the common prime factors to get the GCF.10 12

5 2 3 4

2 2 LCM = 2² x 3 x 5 = 60

2² x 32 x 5

Rod helped his mom plant a vegetable garden. Rod planted a

row every 30 minutes, and his mom planted a row every 20

minutes. If they started together, how long will it be before they both finish a row at the same

time?60 minutes (1 hour)