1. Primes, Factors, & Multiples NOtes

2. Factors

3. Finding Factors
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. 3

4. Factoring Rules 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 4

5. Factoring Rules A number is divisible by …
3, if the sum of its digits is divisible by 3
Example: 81 because = 9 and 9 is divisible by 3 5

6. Factoring Rules A number is divisible by …
4, if the last 2 digits are divisible by 4
Example: 124 because 24 is divisible by 4 6

7. Factoring Rules 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 7

8. Factoring Rules 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 8

9. Factoring Rules 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 9

10. Factoring Rules A number is divisible by …
9, if the sum of the digits is divisible by 9
Example: 468 because = 18 and 18 is divisible by 9 10

11. Factoring Rules A number is divisible by …
10, if the number ends in zero
Example: 50 because the number ends in zero 11

12. Common Factors
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. 12

13. GCF 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.

14. Find the GCF(12, 42, 96)

15. You use the GCF to solve problems like the following
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

16. You use the GCF to solve problems like the following
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

17. Multiples 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 multiples
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44…
6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66…

18. LCM
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…

19. Find the LCM(6, 8, 12)
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…

20. You use the LCM to solve problems like the following
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)

21. You use the LCM to solve problems like the following
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

22. Composites &Primes
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

23. Prime Factorization
Two numbers that are neither prime nor composite: and
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.

24. Finding the Prime Factorization of150
STEPS
Calculations
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.
Since 5 is a prime number we circle it. 6 is a composite number, we repeat Step 1.
Since both 2 and 3 are prime we circle them.
Since all the numbers are broken into prime factors, we use them to write the product.
Then we write the prime factorization in exponential form (using exponents).