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

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The Rules for DivisibilityFocus 3: 6.NS.2

"Divisible By" means "when you divide one number by another the result is a whole number“

(no remainders!)

A number is divisible by……

- The last digit is even (0,2,4,6,8)
- 128Yes129No

- The last digit is 0 or 5
- 175Yes809No

- The number ends in 0
- 220Yes221No

- The sum of the digits is divisible by 3
- 381 (3+8+1=12, and 12÷3 = 4) Yes217 (2+1+7=10, and 10÷3 = 3 1/3) No

- 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

- The number is divisible by both 2and3
- 114 (it is even, and1+1+4=6 and 6÷3 = 2) Yes
- 308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No

- The last 2 digits are divisible by 4
- 1312(12÷4=3) Yes7019 (19÷4=4.75) NO

- The last three digits are divisible by 8
- 109816(816÷8=102) Yes
- 216302(302÷8=37 3/4) No

- 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