1. copyright©amberpasillas2010 RULES FOR DIVISIBILITY #1 A Number Is Divisible By: IF 2 3 4 5 6 8 9 10 The last digit is even (0, 2, 4, 6, 8) The last 2 digits are divisible by 4 The sum of the digits is divisible by 3 The last digit is 0 or 5 It is divisible by 2 and 3 The last 3 digits are divisible by 8 The sum of the digits is divisible by 9 The last digit is 0

2. copyright©amberpasillas2010 IS THE NUMBER DIVISIBLE EXACTLY BY? WRITE yes (y) or no (n) REMEMBER: Show the sums for 3, and show the division for 4 and 8. Number 234568910 1) 360 y 3+6 = 9 y y yy 2)2) 180 2)2) 180 90 y yy 2)2) 60 30 2)2) 30 15 2)2) 90 45 #2

3. FACTOR A Factor is a number that is multiplied by another number to give the product. 7 x 8 = 56 Factors A Factor is the number that divides evenly into another number. 56 ÷ 8 = 7 Factor #3 copyright©amberpasillas2010

4. Prime Numbers- A Prime number is a whole number with exactly 2 factors, one and itself. Example: 17, 3, 2, 11, 13, 5 Composite Numbers- A Composite number is a number that has more than two factors. Example: 9, 30, 64, 8, 40, 69 #4 Prime & Composite copyright©amberpasillas2010

5. Prime Factorization is when you write a number as the product of prime numbers.  Factor Tree 36 #5 2 18 2 9 3 3 Circle the prime numbers

6. copyright©amberpasillas2010 Make A List #6 Make A List Making a list can be helpful to keep track of data and to spot any missing data. To make a list start with the lowest possible factor which is 1. Factors of 36 1 x 36 2 x 18 3 x 12 We know we didn’t miss any Factors because our list is ORGANIZED! Factors of 24 1 x 24 2 x 12 3 x 8 4 x 6 4 x 9 6 x 6

7. copyright©amberpasillas2010 GCF, Make a List Method #1 GCF is the largest number that is a factor of 2 numbers. It is useful to know this for reducing fractions. Ex. Common Factors are 1,2,3,6 GCF= 6 Step 1: List all the factors of both numbers. Step 2: Then find the greatest common factor. #7 Factors of 12 1 x 12 2 x 6 3 x 4 Factors of 30 1 x 30 2 x 15 3 x 10 5 x 6 This method is only useful if both numbers are small

8. copyright©amberpasillas2010 Step 1: Find the prime factorization of the 2 numbers. Step 2: Then multiply their common factors. Factors the 2 numbers have in common are: 2 & 3 Multiply the common factors. #8 12 30 2 6 2 3 2 15 3 5

9. copyright©amberpasillas2010 #9 Multiples A number that is added to itself becomes a multiple. Multiples of 3 = 3, 6, 9, 12, 15, 18... Multiples can go on infinitely forever. It is useful to know this for adding fractions. The least common multiple (LCM) is the least common number that is a multiple of 2 numbers.

10. copyright©amberpasillas2010 LCM Make a List Method # 1 TO FIND THE LCM OF 4 and 12: 2) Find the least multiple that both numbers have in common. 1) List the multiples of both numbers 4 = 4, 8, 12, 16, 20… 12 = 12, 24, 36… LCM is 12 #10 This method is useful if both numbers are small.

11. copyright©amberpasillas2010 1) List the prime factorization to find the LCM. 20 2 10 2 5 18 2 9 3 3 2) Select all common factors once. 3) Select all remaining factors, and multiply. #11 LCM Prime Factorization Method # 2