1. The Rules for Divisibility Focus 3: 6.NS.2

2. Start on a “Fresh Left” page! Heading for your Math Workbook Page "Divisible By" means "when you divide one number by another the result is a whole number“ (no remainders!) A number is divisible by……

3. 2 if…  The last digit is even (0,2,4,6,8)  128 Yes 129 No

4. 5 if…  The last digit is 0 or 5  175 Yes 809 No

5. 10 if…  The number ends in 0  220 Yes 221 No

6. 3 if…  The sum of the digits is divisible by 3  381 (3+8+1=12, and 12÷3 = 4) Yes 217 (2+1+7=10, and 10÷3 = 3 1 / 3 ) No

7. 9 if…  The sum of the digits is divisible by 9  1,629 (1+6+2+9=18, then, 1+8=9) Yes  2,013 (2+0+1+3=6) No

8. 6 if…  The number is divisible by both 2 and 3  114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes  308 (it is even, but 3+0+8=11 and 11÷3 = 3 2 / 3 ) No

9. 4 if…  The last 2 digits are divisible by 4  1312 (12÷4=3) Yes 7019 (19÷4=4.75) NO

10. 8 if…  The last three digits are divisible by 8  109816 (816÷8=102) Yes  216302 (302÷8=37 3 / 4 ) No

11. There’s more!  Not only are there divisibility tests for larger numbers, but there are more tests for the numbers we have shown.  Factors Can Be Useful!! (Factors are the numbers you multiply to get another number.) When a number is divisible by another number... …then it is also divisible by each of the factors of that number.  Example: If a number is divisible by 6, it is also divisible by 2 and 3  Example: If a number is divisible by 12, it is also divisible by 2, 3, 4 and 6