Divisibility Rules & Helpful Hints

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Divisibility for the number 1

  • Numbers that are whole are all divisible by 1
  • Example: 4,325 is divisible by 1

Divisibility for the number 2

  • Numbers are divisible by 2 if the ones digit is evenly divisible by 2.
  • This means…. ALL even numbers (anything ending in 2,4,6, or 8) are divisible by 2.

Divisibility for the number 3

  • Numbers are divisible by 3 if the sum of all the individual digits is evenly divisible by 3.
  • Example: 3,252 (3+2+5+2= 12) 12 is divisible by 3, so 3,252 is divisible by 3.

Divisibility for the number 4

  • Numbers are divisible by 4 if the last two individual digits are divisible by 4.
  • Example: 5,612 (12 are the last two numbers) You can divide 12 by 4, so 5,612 is divisible by 4.
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Divisibility for the number 5

  • Numbers are divisible by 5 if the last digit is a 5 or a 0.
  • Example: 2,105 (ends in a 5) so divisible by 5.  1,790 (ends in a 0) so divisible by 5.           
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Divisibility for the number 6

  • Numbers are divisible by 6 if they are divisible by BOTH 2 and 3.  See rules above.
  • Must be an even number  & sum of the digits is divisible by 3.
  • Example: 4,572 (divisible by 2 because its even & all digits add up to 18, which is divisible by 3) so 4,572 is divisible by 6.
  • Example: 4,629 (NOT divisible by 2, but all digits add up to 21, which is divisible by 3) Since not divisible by both 2 & 3, 4,629 is NOT divisible by 6.                                                                                       
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Divisibility for the number 7

  •  Numbers are divisible by 7 if you take the last digit off, double that digit and subtract from the remaining number.
  • Example: 6,104 (take 4 off end of number, double it which equals 8) 610-8=602. (you may need to repeat process twice) 602 (take 2 off end of number & double it to get 4) 60-4=58, which is NOT divisible by 7, so 6,104 is NOT divisible by 7. 
  • Example: 357 (take 7 off end, double it which equals 14) 35-14=21 Since 21 is divisible by 7, then 357 is divisible by 7.
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Divisibility for the number 8

  • Numbers are divisible by 8 if the last three digits are evenly divisible by 8.
  • Example: 7,624 (624 is divisible evenly by 8), so 7,624 is divisible by 8.
  • Example: 4008 (008 is divisible by 8), so 4008 is divisible by 8.
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Divisibility for the number 9

  • Numbers are divisible by 9 if you add up ALL of the digits in the number & the sum is divisible by 9.
  • Example: 2,342,880 (2+3+4+2+8+8+0= 27) 27 is divisible by 9, so 2,342,880 is divisible by 9.
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Divisibility for the number 10

  • Numbers are divisible by 10 if the number ends in 0.
  • Example: 3,450 (ends in 0) so it’s divisible by 10.
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Divisibility for the number 11

  • Numbers are divisible by 11 if you sum every second digit and subtract all the other digits & answer is 0 or divisible by 11.
  • Example: 1,364 (3+4)-(1+6)= 7-7= 0, so yes, 1,364 is divisible by 11.
  • Example: 5,326 (3+6)-(5+2)= 9-7= 2, so NO, 5,326 is NOT divisible by 11.
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Divisibility for the number 12

  • Numbers are divisible by 12 if it is divisible by BOTH 3 and 4. (See examples above)
  • Numbers are divisible by 3 if the sum of all the individual digits is evenly divisible by 3.
  • Numbers are divisible by 4 if the last two individual digits are divisible by 4
  • Example: 648 (By 3: 6+4+8=18, yes 18 divisible by 3; By 4:48÷4=12, yes) so, YES 648 is divisible by 12.
  • Example: 237 (By 3: 2+3+7= 12, yes 12 divisible by 3; By 4: 37÷4= 9 1/4, no) so NO, 237 isn’t divisible by 12.
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