We often need to know quickly if one number is a factor of another number.

Knowing the following rules can make your factoring tasks much easier.

A number is divisible by …

2, if it ends in an even number in the ones place (0, 2, 4, 6, 8)

Example: 558 because there is an 8 in the ones place

A number is divisible by …

3, if the sum of its digits is divisible by 3

Example: 81 because 8 + 1 = 9 and 9 is divisible by 3

A number is divisible by …

4, if the last 2 digits are divisible by 4

Example: 124 because 24 is divisible by 4

A number is divisible by …

5, if the ones digit is a 0 or a 5

Example: 1125 because there is a 5 in the ones place

A number is divisible by …

6, if the number is divisible by 2 AND 3

Example: 48 There is an 8 in the ones place so it is divisible by 2 8 + 4 = 12 and 12 is divisible by 3

A number is divisible by …

8, if the last 3 digits are divisible by 8

Example:1240 because there is 240 is divisible by 8

A number is divisible by …

9, if the sum of the digits is divisible by 9

Example: 468 because 4 + 6 + 8 = 18 and 18 is divisible by 9

A number is divisible by …

10, if the number ends in zeroExample: 50 because the number ends in zero

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.

Finding 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

12 42 961 12 1 42 1

962 6 2 21 2 483 4 3 14 3 32

6 7 4 24 6 16

8 12

Mr. Grover wants to make shelves for his garage using an 18-foot

board and a 36-foot board. He will cut the boards to make shelves of the same length and wants to use

all of both boards. Find the greatest possible length of each shelf.

18 ft

The SGB reps are making spirit ribbons. Blue ribbon comes in a 24 inch spool, red ribbon comes in a 30 inch spool, and gold ribbon comes in a 36 inch spool. The SGB reps want to cut

strips of equal length, using the entire spool of each ribbon. What is the

length of the greatest piece of ribbon that can be cut from each spool?

6 inches

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

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

Common Multiples: multiples that two or more numbers have in common.Example: 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, 54, 60, 66…

• Least Common Multiple: the smallest multiple that two numbers have in common, excluding zero.Finding 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…

6 : 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66 …

8 : 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88 ….

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

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)

Three bike riders ride around a circular path. The first rider circles the path in 12 minutes, the second in 18 minutes, and the third in 24 minutes. If they all start at the

same place at the same time, and go in the same direction, after how

many minutes will they meet at the starting point?

72 minutes

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.

2. Since 5 is a prime number we circle it (this means it is one of the prime factors of 150). 30 is a composite number, we repeat Step 1.

3. Since 5 is a prime number we circle it. 6 is a composite number, we repeat Step 1.

4. Since both 2 and 3 are prime we circle them.

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

6. Then we write the prime factorization in exponential form (using exponents).