#7**+10 **

I was deriving thejamesmachine's method for determining if a number is divisible by 7. Here's how he expressed it

*For seven:*

*Take the last digit, double it, and subtract it from the rest of the number. If the answer is divisible by 7 (including 0), then the number is also divisible by 7:*

*861:86-1x2=84*

*84/7=12*

.

Alan
May 30, 2015

#1**+5 **

624 =

312 * 2 =

156 * 2 * 2 =

78 * 2 * 2 * 2 =

39 * 2 * 2 * 2 * 2

13 * 3 * 2 * 2 * 2 * 2 =

2^4 * 3 * 13

CPhill
May 29, 2015

#2**+8 **

http://web2.0calc.com/questions/what-will-go-into92

Check the link out

thejamesmachine
May 29, 2015

#3**+5 **

Thanks, thejamesmachine for that link....I didn't know the "trick" for testing 7 as a factor.........

{Now....I want to see if I can figure out WHY that works.......LOL!!! )

CPhill
May 29, 2015

#4**+5 **

Yes Chris, I agree, that would be a good challange :)

I had not heard of it before james put it on the forum either . Thanks James

Melody
May 30, 2015

#5**+5 **

Is N exactly divisible by 7?

Let N = 10n + a where n and a are integers and a is in the units position.

Construct M = n - 2a (i.e. twice the units value subtracted from what's left, where what's left is considered to be a number in its own right).

If M is exactly divisible by 7 then we can write n - 2a = 7m where m is an integer.

So n = 7m + 2a

In that case N = 10(7m + 2a) + a or N = 70m + 21a

So N/7 = 10m + 3a and since m and a are integers the resulting value of N/7 is an integer. i.e. N is exactly divisible by 7 with no remainder.

.

Alan
May 30, 2015

#7**+10 **

Best Answer

I was deriving thejamesmachine's method for determining if a number is divisible by 7. Here's how he expressed it

*For seven:*

*Take the last digit, double it, and subtract it from the rest of the number. If the answer is divisible by 7 (including 0), then the number is also divisible by 7:*

*861:86-1x2=84*

*84/7=12*

.

Alan
May 30, 2015