212 Appendix D
For instance, let’s check if 15,476 is divisible by four. Th e tens digit,
7, is odd, so we carry 1 to the units digit, 6, to make 16. Sixteen is
evenly divisible by 4, so 15,476 is evenly divisible by 4.
Is 593,768 divisible by 4? Th e tens digit, 6, is even, so we can ignore
it. Th e units digit, 8, is evenly divisible by 4, so 593,768 is evenly
divisible by 4.
Divisibility by 5: Five is easy. If the last digit of the number is 5 or
0, then the number is evenly divisible by 5.
Divisibility by 6: If the number is even and the sum of the digits is
divisible by 3, then the number is also divisible by 6 (because 6 is 2
times 3). For instance, the digit sum of 54 is 9 (5 + 4 = 9), which is
divisible by 3, and 54 is an even number, so 54 is divisible by 6.
Divisibility by 7: You will have to read my book Speed Mathematics
for a full explanation of this, but here is a quick introduction. You
multiply the fi nal digit of the number by 5 and add the answer to
the number preceding it. If the answer is divisible by 7, then the
number is divisible by 7. For example, let’s take 343. Th e fi nal digit
is 3. We multiply 3 by 5 to get 15. We add 15 to the number in
front of the 3, which is 34, to get 49. Th en, 49 is evenly divisible by
7, so 343 is as well.
Divisibility by 8: If the fi nal three digits are evenly divisible by 8, then
the number is evenly divisible by 8 (because 1,000 = 8 × 125).
Here we have an easy check similar to the check for 4. If the hundreds
digit is even, it can be ignored. If it is odd, add 4 to the fi nal two
digits of the number. Th en, if the fi nal two digits are divisible by 8,
the number is divisible by 8.
For example, is the number 57,328 divisible by 8? Th e hundreds
digit, 3, is odd, so we add 4 to the fi nal two digits, 28. So, 28 + 4 =
- Th irty-two is divisible by 8, so 57,328 is evenly divisible by 8.
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