Tests for Divisibility 213
Divisibility by 9: If the digit sum adds up to 9 or is evenly divisible
by 9, the number is divisible by 9.
Divisibility by 10: If the number ends with a 0, the number is
divisible by 10.
Divisibility by 11: If the diff erence between the sum of the evenly
placed digits and the oddly placed digits is a multiple of 11, the
number is evenly divisible by 11.
Divisibility by 12: If the digit sum is divisible by 3 and the last two
digits are divisible by 4, the number is divisible by 12.
Divisibility by 13: Again, a full explanation is in Speed Mathematics.
Th e rule for 13 is similar to the rule for 7. You multiply the fi nal digit
of the number by 4 and add the answer to the number preceding it.
If the answer is divisible by 13, then the number is divisible by 13.
For example, let’s take 91. Th e fi nal digit is 1. We multiply 1 by 4 to
get 4. We add 4 to the number in front of the 1, which is 9, to get
- And 13 is evenly divisible by 13, so 91 is as well.
Let’s try it again with 299. Is 299 evenly divisible by 13? It is hard
to tell without actually doing a division. We multiply the fi nal digit,
9, by 4 to get an answer of 36. Add 36 to the 29 in front of the 9 to
get 65. You may recognize that 65 is 13 × 5, but if not, carry out the
operation again. We are now checking 65. Multiply 5 by 4 to get
- Add 20 to the 6 in 65 to get 26. We can see that 26 is 2 × 13, so
there is no doubt now that 299 is evenly divisible by 13.
It is often useful to know if a number has factors that can be used
to simplify a fraction or to simplify a multiplication or division
problem.
bbapp04.indd 213app 04 .indd 213 1 1/5/07 11:36:17 AM/ 5 / 07 11 : 36 : 17 AM
