is there a faster way to make a divisibilty test for 7 than natually dividing it?

Answer 1

Good question. And there is a way of doing it that I don't pretend to understand off the top of my head that goes like this:

Double the last digit and subtract it from the remaining leading truncated number. If the result is divisible by 7, then so was the original number. Apply this rule over and over again as necessary. Example: 826. Twice 6 is 12. So take 12 from the truncated 82. Now 82-12=70. This is divisible by 7, so 826 is divisible by 7 also.

I found it by googling "divisibility test for 7" .

HTH

Answer 2

Actually, there is one.
We call it the ladder rule.
Take the last digit. Multiply it by 5. Then add the
product to the number without its last digit.
If the resulting number is big, repeat the process.
When you get a small enough number, check
it for divisibility by 7. If the answer is "yes", then
all the results on your ladder are multiples of 7.
If the answer is "no", none of them are.
Simple example: Is 126 a multiple of 7?
Well, 6* 5 = 30, and 12 + 30 = 42.
Since 42 = 6*7, 126 is indeed a multiple of 7.
Interestingly enough, there is a similar
divisibility rule for any whole number ending
in 1, 3, 7 or 9. The only thing that changes is
the multiplier.
For example, if you want to test for divisibility by 13,
use the above rule, but multiply the last digit
by 4 instead of 5.
Some other multipliers:
no. multiplier
17 12
19 2
21 19
23 7
27 19
29 3
See if you can find a pattern for guessing the multiplier
for any whole number ending in 1, 3, 7 or 9!

Answer 3

Test for divisibility by 7. Double the last digit and subtract it from the remaining leading truncated number. If the result is divisible by 7, then so was the original number. Apply this rule over and over again as necessary. Example: 826. Twice 6 is 12. So take 12 from the truncated 82. Now 82-12=70. This is divisible by 7, so 826 is divisible by 7 also.

I copied and pasted this directly from a website.

Answer 4

There are several ways of testing for divisibility by 7, including the one they cut and pasted above, but I don't think any of them are really faster than just doing the division by hand. That's why instructors generally don't teach them to students. Sorry. :-)

Answer 5

not that I know of