Difference between revisions of "Divisibility rules"
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| − | == | + | == Divisibility Rule for 2 and Powers of 2 == |
A number is divisible by <math>2^n</math> if the last <math>{n}</math> digits of the number are divisible by <math>2^n</math>. | A number is divisible by <math>2^n</math> if the last <math>{n}</math> digits of the number are divisible by <math>2^n</math>. | ||
| − | == | + | == Divisibility Rule for 3 == |
A number is divisible by 3 if the sum of its digits is divisible by 3. | A number is divisible by 3 if the sum of its digits is divisible by 3. | ||
| − | == | + | == Divisibility Rule for 5 and Powers of 5 == |
A number is divisible by <math>5^n</math> if the last n digits are divisible by that power of 5. | A number is divisible by <math>5^n</math> if the last n digits are divisible by that power of 5. | ||
| − | == | + | == Divisibility Rule for 9 == |
A number is divisible by 9 if the sum of its digits is divisible by 9. | A number is divisible by 9 if the sum of its digits is divisible by 9. | ||
| − | == | + | == Divisibility Rule for 11 == |
A number is divisible by 11 if the alternating sum of the digits is divisible by 11. | A number is divisible by 11 if the alternating sum of the digits is divisible by 11. | ||
| − | == | + | == Divisibility Rule for 7 == |
Rule 1: Partition <math>n</math> into 3 digit numbers from the right (<math>d_3d_2d_1,d_6d_5d_4,\dots</math>). If the alternating sum (<math>d_3d_2d_1 - d_6d_5d_4 + d_9d_8d_7 - \dots</math>) is divisible by 7, then the number is divisible by 7.<br> | Rule 1: Partition <math>n</math> into 3 digit numbers from the right (<math>d_3d_2d_1,d_6d_5d_4,\dots</math>). If the alternating sum (<math>d_3d_2d_1 - d_6d_5d_4 + d_9d_8d_7 - \dots</math>) is divisible by 7, then the number is divisible by 7.<br> | ||
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| − | == | + | == Divisibility Rule for 13 == |
See rule 1 for divisibility by 7. A number is divisible by 13 if the same specified sum is divisible by 13. | See rule 1 for divisibility by 7. A number is divisible by 13 if the same specified sum is divisible by 13. | ||
Revision as of 15:38, 28 June 2006
These divisibility rules help determine when integers are divisible by particular other integers.
Contents
Divisibility Rule for 2 and Powers of 2
A number is divisible by 
if the last 
digits of the number are divisible by .
Divisibility Rule for 3
A number is divisible by 3 if the sum of its digits is divisible by 3.
Divisibility Rule for 5 and Powers of 5
A number is divisible by 
if the last n digits are divisible by that power of 5.
Divisibility Rule for 9
A number is divisible by 9 if the sum of its digits is divisible by 9.
Divisibility Rule for 11
A number is divisible by 11 if the alternating sum of the digits is divisible by 11.
Divisibility Rule for 7
Rule 1: Partition 
into 3 digit numbers from the right (
). If the alternating sum (
) is divisible by 7, then the number is divisible by 7.
Rule 2: Truncate the last digit of , and subtract twice that digit from the remaining number. If the result is divisible by 7, then the number is divisible by 7. This process can be repeated for large numbers.
Divisibility Rule for 13
See rule 1 for divisibility by 7. A number is divisible by 13 if the same specified sum is divisible by 13.
