2. Although 360 (three sixty, for short) was new to his school and had only formed a few new friendships, he decided that History was his favorite subject at Digit Middle School. His teacher always seemed to have such interesting stories to tell and today she had assigned a project to the class that 360 could hardly wait to start. The project demanded that each student look back into their family history to find out what numbers were a key factor in their formation and development.

3. This is more commonly known as Divisibility. 360’s teacher had given each student a list of divisibility rules that each student would have to follow to find out whether or not a particular number was a member of his/her family tree.

4. To find out if a number was a key factor in 360’s development, he could divide himself by the number to see if there was a remainder. Ex. Is 360 divisible by 3? 120 3 360 3 0 6 6 0 0 - 0 Yes, but there has got to be a better way. This takes a lot of time!

5. 360’s teacher shared with the students some rules that make it easier to find out if a number plays apart in the formation of another. If the number ends in a 0, 2, 4, 6, or 8, it is divisible by 2! Example: 26 YES! Example: 843 NO! Is 360 divisible by 2? Is 2 a factor in his formation? YES!

6. Here is the rule the teacher shared to help 360 figure out if he is divisible by 3! A number is divisible by 3 if the sum of all of the digits is divisible by 3. Example: 146 (1+4+6=11; 11/3= 3 R2) NO! It is not divisible by 3! Was 3 a factor in 360’s formation? (3+6+0= 9; 9/3 = 3 YES!) 360 can add 3 to his family tree.

7. To see if 4 is a key factor, 360 needs to see If the number formed by the last two digits is divisible by 4, then the entire number is divisible by 4. Example: 520 (20/4=5 with no remainder) YES! 520 is divisible by 4. Example: 1,025 (25/4= 6 R1) No, 1,025 is not divisible by 4. How about 360? Can he add 4 to his list? 360 4 60 = 15 YES!

8. 5 is an easy one. 360 already knew the rule. If the number ends with a 0 or 5, it is divisible by 5. Example: 27 (7 is not a 0 or a 5) NO! 27 is not divisible by 5. Example: 2,895 (The last number is a 5) YES! 2,895 is divisible by 5. Is 360 divisible by 5? YES! And the family grows!

9. The rule 360 learned for 6 is If the number is divisible by 2 AND 3, then it is divisible by 6. First test 2; Then test 3! Example: 90 (Last number is a 0, so it is divisible by 2. 9+0=9, 9/3=3 no remainder, so it is divisible by 3.) YES! 90 is divisible by 6! Is 360 going to be able to include 6? 2 – ends in even number 3 – sum of the digits is divisible by 3 360 can include 6 in his list. 6 in his list.

10. 360 could hardly contain himself as he looked back over the multitude of numbers he had found to be a part of what he thought to be such meager beginnings. The rule for 9 is The number is divisible by nine if the sum of the digits is divisible by 9. Example: 82 (8+2=10, 10/9= 9 R1) NO! 82 is not divisible by 9. Example: 117 (1+1+7= 9, 9/9=1 no remainder) YES! 117 is divisible by 9! 3+6+0 = 9, 9/9= 1 Once again to 360’s surprise, 9 would also join his family.

11. 360 wondered if he would be able to add 10 to his list. A number is divisible by 10 if the last digit is a zero! Example: 298 No! 298 is not divisible by 10. 360 can hardly believe what he read. Could this be true? YES! His last number is a 0.

12. 360’s teacher was so impressed with how well his project turned out that she asked 360 to help his classmates research their family’s history. Help 360 follow the Rules of Divisibility to find key factors in the formation of his classmates. 2 – ends in an even number 1876 Yes 3 – sum of the digits divisible by 3 No 4 – 4 will divide evenly into the last 2 digits 2 digitsYes (1+8+7+6 =22; 22/3= 7 r1) 5 – ends in a 5 or 0 No 76/4 = 19 6- divisible by 2 AND 3 (2 – yes, 3 – no) No

13. 360’s teacher also told him that any number that has more than 2 factors is called a Composite Number. Ex: 8Factors of 8: 1,2,4,8 (1 x 8, 2 x 4) Ex: 12Factors of 12: 1,2,3,4,6,12 (1 x 12, 2 x 6, 3 x 4) Is 360 composite? Composite Numbers

14. Numbers that only have 2 factors (the number 1 and itself) are called a Prime Number. Ex: 5Factors of 5: 1,5 (because only 1 x 5 = 5) Ex: 11Factors of 11: 1,11 (because only 1 x 11 = 11) Prime Numbers

15. Can you tell if these numbers are Prime or Composite? 1)13 2)15 3)54 4)79 5)112 *Don’t forget to use your Divisibility Rules! prime Composite (3 x 5) Composite ( 2 x 56) prime Composite (6 x 9)

16. Rules of Divisibility 2 Ends in an even number 3 Sum of the digits divisible by 3 Last 2 digits divisible by 4 4 Ends in 0 or 5 5 Divisible by 2 and 3 6 Sum of the digits divisible by 9 9 Ends in 0 10