2. division algorithm Before we study divisibility, we must remember the division algorithm. r dividend = (divisor ⋅ quotient) + remainder

3.  A number is divisible by another number if the remainder is 0 and quotient is a natural number.  A natural number is any whole number 0 or greater.  A negative number is not a natural number.

4.  A natural number is any whole number 0 or greater. What is NOT a natural number?  A negative number is NOT a natural number.  A fraction or decimal is NOT a natural number.

5.  If a number is divided by itself then quotient is 1.  If a number is divided by 1 then quotient is itself.  If 0 is divided by any natural number then quotient is 0.  If any number is divided by zero then quotient is undefined. (You cannot divide a number by 0)

6.  Divisibility by 2: All even numbers are divisible by 2 Example: Check if each number is divisible by 2. a.108 b. 466c. 87,682 d. 68,241 e. 76 543 010

7.  Divisibility by 3: Add up all the digits in the number. If the sum is divisible by 3, then the number is divisible by 3. Example: Determine whether the following numbers are divisible by 3 or not. a) 7605 b) 42,145 c) 555,555

8.  Divisibility by 4: A number is divisible by 4 if the last two digits of the number are 00 or a multiple of 4. Example: Determine whether the following numbers are divisible by 4 or not. a) 7,600 b) 47,116 c) 62,549,093

9. Divisibility by 5: A natural number is divisible by 5 if its last digit is 0 or 5. Examples: 25 140 67,345

10. Divisibility by 6: A number is divisible by 6 if it is divisible by both 2 and 3. Example: Determine whether the following numbers are divisible by 6 or not. a) 4608 b) 69,030 c) 222,522

11. Divisibility by 9: A natural number is divisible by 9 if the sum of the digits of the number is divisible by 9. Examples—Determine if the following numbers are divisible by 9. 738 9,657 54,542

12. Divisibility by 10: A natural number is divisible by 10 if its units (last) digit is 0. Example: is 3700 divisible by 10?