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Divisibility Rules

Divisibility Rules. “How do I know if I can divide this number?”. What does “divisible” mean?. If a number has a remainder of “0” when divided by another number, then it is said to be divisible by that number. Ex. 16 / 2 = 8 Therefore, 16 is divisible by 8. Is this number divisible by 2?.

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Divisibility Rules

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  1. Divisibility Rules “How do I know if I can divide this number?”

  2. What does “divisible” mean? • If a number has a remainder of “0” when divided by another number, then it is said to be divisible by that number. • Ex. 16 / 2 = 8 • Therefore, 16 is divisible by 8.

  3. Is this number divisible by 2? • A number that ends in 2, 4, 6, 8, or 0 is divisible by 2.

  4. Is this number divisible by 3? • If the sum of the digits is divisible by three, then so is the number. • Ex. 24 => 2 + 4 = 6 , is 6/3…yes; therefore, 24 is divisible by 3. • Ex. 342=> 3 + 4 + 2 = 9 and 9/3; therefore, 342 is divisible by 3.

  5. Is this number divisible by 4? • If the last two digits are divisible by 4, then the whole number is divisible by 4. • Ex. 4324…the last two digits are 24 and 24/4 = 6; therefore, 4324 is divisible by 4.

  6. Is this number divisible by 5? • If the number ends in 5 or 0, then it is divisible by 5. (If the ones digit is 5 or 0, then it is divisible by 5.) • Ex. Are the following numbers divisible by 5? • 5 yes -- 25 yes • 15 yes -- 516 no • 18no -- 348925415 yes

  7. Is this number divisible by 6? • If the number is divisible by 2 and 3, then it is divisible by 6. • Ex. 216 • /2 (ends in 6) yes • /3 (2+1+6=9) yes • /6 ( /2 and /3) YES

  8. Is this number divisible by 7? • The rule is too way too LONG to remember…therefore, divide it out and see is you get a remainder.

  9. Is this number divisible by 8? • If the number formed by the last 3 digits is divisible by 8, then the whole number is divisible by 8. • Ex. 6320 … 320/8 = 40; therefore, 6320 is divisible by 8.

  10. Is this number divisible by 9? • If the sum of the digits is 9, then the number is divisible by 9. • Ex. 5130 5 + 1 + 3+ 0 = 9; therefore, 5130 is divisible by 9.

  11. Is this number divisible by 10? • If the one’s digit is 0, then the number is divisible by 10. • 100 yes • 150 yes • 80000 yes • 141352 NO • 687200 yes • 741812.9 NO

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