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Here's a simple trick, very similar to the trick for telling if a number is divisible by 9 (adding up the digits). If you can do some simple arithmetic in your head, you don't even need a calculator!
Suppose you want to know if this big, long number is divisible by 37:
3018302856381
Step 1: Add up the BLN three digits at a time:
3 + 018 + 302 + 856 + 381 = 1560
Step 2: If the number is still bigger than 999, repeat the process:
1 + 560 = 561
>>>If this number is divisible by 37, then so is your original BLN!<<<
But how do you tell if this result is divisible by 37? Well, there are only 27 multiples of 37 under 1000, so you memorize them all! But don't worry too much, it's even easier than that, really. Nine of them are REALLY easy: 111, 222, 333, ..., and 999. And you can get all the rest by adding or subtracting 37 to one of these. 111+37=148, 222-37=185, and so on.
Finishing our example, 561 is not 37 away from 555 or its buddies, so 3018302856381 is not a multiple of 37.
Let's try another example:
41484438628
41 + 484 + 438 + 628 = 1591
1 + 591 = 592
592 is 555 + 37
So 41484438628 is a multiple of 37!
Originally posted at 2:26PM, 11 July 2006 PDT
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mag3737 edited this topic 60 months ago.
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Interesting trick... I'm starting to think there's more to 37 than meets the eye.
Posted 72 months ago.
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My brain hurts, but I have at least figured out 74 - it's a start :-)
Posted 70 months ago.
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Great!
:))
Posted 68 months ago.
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What I did:
Use MS Excel.
Type the following in cell A1:
=ROW()*37
Copy cell A1.
Select the whole column A by clicking on the column name.
Paste (ctrl-v)
You now have 65536 multiples of 37.
This is fun! I didn't know I had eight multiples of 37.
Originally posted 66 months ago.
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designwallah edited this topic 66 months ago.
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ah, well, if that's your bag, here's a slightly faster way (saves the "copy" step):
Type the following in A1: =row()*37
Click on the 'A' to select the column
Type Ctrl-D to replicate the formula
Posted 66 months ago.
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Ahhhhh!
Posted 66 months ago.
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you can do it without using the mouse in the same number of steps (i love keyboard shortcuts):
Type =row()*37 in the first cell *but don't hit ENTER*
Type Ctrl+Shift+Down Arrow
Type Ctrl-D
Posted 66 months ago.
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Numbers give me a headache. ;-)
Posted 65 months ago.
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That's easy. Just open the notepad (or vi) and type:
#include
int main(void)
{
unsigned int i;
FILE* fp;
fp = fopen("multiples.txt", "rw");
for(i=37;i<0xFFFF;i+37)
{
fprintf(fp, "%d ", i);
}
fclose(fp);
return 0;
}
Save the file as multiples.c, open the command prompt (winkey + r and type cmd) or a terminal and type on the directory you saved the file:
gcc -o multiples multiples.c
multiples (or ./multiples)
and it's done. You now have a text file with ALL 16bit numbers who are multiples of 37. You just have to open it when you have a new number photo and search.
=)
Posted 65 months ago.
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of course, my original trick is better than all of these clever programming techniques when all you have to work with is your brain. ;-)
Posted 65 months ago.
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lol
Posted 65 months ago.
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Interestingly, although perhaps not so helpful, I noticed that 3 digit multiples can be rearranged to make another multiple. If you take the left side digit and move it to the right, you have another multiple of 37.
e.g. 148 - move the 1 to the right side becomes 481
185 becomes 851
296 --> 962; 259 --> 592, etc.
If you need any more useless information, let me know. :-)
Posted 47 months ago.
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i've always found this trick helpful, in addition to the one i gave above. it's another way that you can avoid having to memorize all 27 three-digit multiples.
it shouldn't take too much further thought to convince yourself that same fact is true for any multiple of 37 whose length is a multiple of 3. to take a six-digit example from the pool, all five "rotations" of it are also multiples of 37:
434861 >> 348614 >> 486143 >> 861434 >> 614348 >> 143486
Posted 47 months ago.
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And all these years I just liked the number 37 because it has visual appeal to me. 8-|
Posted 47 months ago.
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my mobile phone has a calculator... I could use that!
Posted 45 months ago.
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That's a great trick! For example google calculator can't deal with too big numbers and can give some wrong answers (try 8453309876/37 from oyster card :P). This trick reduces the number a lot and I can use google again :-)
Posted 39 months ago.
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"Here's a simple trick, very similar to the trick for telling if a number is divisible by 9 (adding up the digits). If you can do some simple arithmetic in your head, you don't even need a calculator!"
Clever. This works because 37 is a factor of 999. In general, if the sum of digits of a number in Base N is a multiple of a factor of (N-1) then the original number is a multiple of a factor of (N-1). You can use the same final sum for this problem to find multiples of 27.
Posted 37 months ago.
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exactly. so when that girl you are trying to impress decides that 37 is too boring (perish the thought!), try calculating whether some big long number is divisible by 271, by grouping the digits 5 at a time. (99999 is divisible by 271.)
Posted 37 months ago.
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??? That took me a good 5 minutes to wrap my head around that one Eli.
Using Tom's technique, you better limit yourself to dating math/engineering majors.
On a somewhat unrelated note, I missed a great shot of a guy's t-shirt that said "333 - half evil".
(50-50 chance he would have punched me for taking his picture right?)
Posted 36 months ago.
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haha...yeah, maybe you are lucky you missed it.
Posted 36 months ago.
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