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Divisibility Rules

Divisibility Rules. Before we study divisibility, we must remember the division algorithm. r. dividend = (divisor ⋅ quotient) + remainder. Divisibility. A number is divisible by another number if the remainder is 0 and quotient is a natural number.

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Divisibility Rules

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  1. Divisibility Rules

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

  3. Divisibility • 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. What is a natural number? • A natural number is any whole number0 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. Division Rules • 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 Rules • Divisibility by 2: All even numbers are divisible by 2 Example: Check if each number is divisible by 2. 108 b. 466 c. 87,682 d. 68,241 e. 76 543 010

  7. Divisibility Rules Example: Determine whether the following numbers are divisible by 3 or not. 7605 42,145 c) 555,555 • 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.

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

  9. Divisibility Rules 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 Rules 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. 4608 69,030 c) 222,522

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

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