4 ms·

Clever but most people won't remember these tricks. I for one would appreciate a refresher on the other divisibility rules/tricks.

ramidarigaz 16y ago
If the last two digits are divisible by four, the entire number is divisible by four. For instance: 62857724. 24 is divisible by four, so the whole thing is.
jackowayed 16y ago
I know: * 2 - if it ends in 0,2,4,6,8, it's divisible by 2 * 3 - if the sum of the digits is divisible by 3, so is the number * 4 - Ignore everything but the last 2 digits. If the last 2 digits make a number that's divisible by 4, the whole number is (eg. anything ending in 52 is divisible by 4 because 52 is divisible by 4) * 5 - If it ends in 0 or 5, it's divisible by 5. * 6 - do an and of the 2 and 3 tests. * 8 - Same as the 4 test, only last 3 digits. * 9 - same as 3, only the digit sum needs to be divisible by 9 instead of 3 * 10 - If it ends in 0, it's divisible by 10. So I guess the only one I don't know is 11.
- skmurphy 16y ago
  11 = add the first, third, fifth, etc.. digits, if the sum matches that for the second, fourth, sixth, etc.. then the number is divisible by 11.
  - TheNewAndy 16y ago
    Not quite: 5060 is an exception to your rule. As described before, if (even digit sum) - (odd digit sum) is divisible by 11, then the number is divisible by 11.
    - skmurphy 16y ago
      If you are not careful you will learn something new. Thanks for the tip.
spicyj 16y ago
I do math contests competitively, so I remember these things. Here are some rules: Divisibility by 2: Last digit is divisible by 2 (0, 2, 4, 6, or 8). Divisibility by 3: Sum of digits is divisible by 3. (You can repeatedly sum the digits until the sum is small enough to manage easily.) Divisibility by 4: Last two digits are divisible by 4 (00, 04, 08, 12, ...). If you don't know your multiples of four, you can divide the two digits by 2 and then see if it's even. Divisibility by 5: Last digit is divisible by 5 (0 or 5). Divisibility by 6: Divisible by 2 and by 3. (Works similarly for all composite numbers, of course. Like 10, 14, 15, etc. Make sure the factors you're checking are relatively prime (share no common factors), or it won't work. For example, divisibility by 2 and 6 does not imply divisibility by 12.) Divisibility by 8: Last three digits are divisible by 8 (000, 008, 016, ...). Probably faster to divide the last three by 2 at least once then check divisibility by 4. Divisibility by 9: Sum of digits is divisible by 9. (You can repeatedly sum the digits until the sum is small enough to manage easily.) Divisibility by 11: Alternating sum of digits is divisible by 11. (Almost always turns out to be -11, 0, or 11. Example: 66374. 6 - 6 + 3 - 7 + 4 = 0, so 66374 is divisible by 11.)
- kijinbear 16y ago
  > relatively prime Do primes come in degrees these days?
  - sid0 16y ago
    I'm not sure if this is humour or not, but "relatively prime" or "coprime" means that the two numbers have GCD 1.
- omaranto 16y ago
  Seeing this list of silly things one might find useful in high school math contests made me nostalgic for those days...
  - jacquesm 16y ago
    They're not that silly actually. Division is the most 'complicated' of the arithmetic operations and if you rely on doing sums in your head frequently then knowing such shortcuts can speed up the calculations considerably. It also helps in checking results of other calculations.
anorwell 16y ago
Here's how to divide by 3: http://www.math.dartmouth.edu/~doyle/docs/three/three.pdf http://www.math.dartmouth.edu/~doyle/docs/three/three.pdf
senki 16y ago
The Wikipedia has a good article: http://en.wikipedia.org/wiki/Divisibility_rule http://en.wikipedia.org/wiki/Divisibility_rule

ramidarigaz 16y ago

If the last two digits are divisible by four, the entire number is divisible by four. For instance: 62857724. 24 is divisible by four, so the whole thing is.

jackowayed 16y ago

I know: * 2 - if it ends in 0,2,4,6,8, it's divisible by 2 * 3 - if the sum of the digits is divisible by 3, so is the number * 4 - Ignore everything but the last 2 digits. If the last 2 digits make a number that's divisible by 4, the whole number is (eg. anything ending in 52 is divisible by 4 because 52 is divisible by 4) * 5 - If it ends in 0 or 5, it's divisible by 5. * 6 - do an and of the 2 and 3 tests. * 8 - Same as the 4 test, only last 3 digits. * 9 - same as 3, only the digit sum needs to be divisible by 9 instead of 3 * 10 - If it ends in 0, it's divisible by 10. So I guess the only one I don't know is 11.

skmurphy 16y ago
11 = add the first, third, fifth, etc.. digits, if the sum matches that for the second, fourth, sixth, etc.. then the number is divisible by 11.
- TheNewAndy 16y ago
  Not quite: 5060 is an exception to your rule. As described before, if (even digit sum) - (odd digit sum) is divisible by 11, then the number is divisible by 11.
  - skmurphy 16y ago
    If you are not careful you will learn something new. Thanks for the tip.

spicyj 16y ago

I do math contests competitively, so I remember these things. Here are some rules: Divisibility by 2: Last digit is divisible by 2 (0, 2, 4, 6, or 8). Divisibility by 3: Sum of digits is divisible by 3. (You can repeatedly sum the digits until the sum is small enough to manage easily.) Divisibility by 4: Last two digits are divisible by 4 (00, 04, 08, 12, ...). If you don't know your multiples of four, you can divide the two digits by 2 and then see if it's even. Divisibility by 5: Last digit is divisible by 5 (0 or 5). Divisibility by 6: Divisible by 2 and by 3. (Works similarly for all composite numbers, of course. Like 10, 14, 15, etc. Make sure the factors you're checking are relatively prime (share no common factors), or it won't work. For example, divisibility by 2 and 6 does not imply divisibility by 12.) Divisibility by 8: Last three digits are divisible by 8 (000, 008, 016, ...). Probably faster to divide the last three by 2 at least once then check divisibility by 4. Divisibility by 9: Sum of digits is divisible by 9. (You can repeatedly sum the digits until the sum is small enough to manage easily.) Divisibility by 11: Alternating sum of digits is divisible by 11. (Almost always turns out to be -11, 0, or 11. Example: 66374. 6 - 6 + 3 - 7 + 4 = 0, so 66374 is divisible by 11.)

kijinbear 16y ago
> relatively prime Do primes come in degrees these days?
- sid0 16y ago
  I'm not sure if this is humour or not, but "relatively prime" or "coprime" means that the two numbers have GCD 1.
omaranto 16y ago
Seeing this list of silly things one might find useful in high school math contests made me nostalgic for those days...
- jacquesm 16y ago
  They're not that silly actually. Division is the most 'complicated' of the arithmetic operations and if you rely on doing sums in your head frequently then knowing such shortcuts can speed up the calculations considerably. It also helps in checking results of other calculations.

anorwell 16y ago

Here's how to divide by 3: http://www.math.dartmouth.edu/~doyle/docs/three/three.pdf http://www.math.dartmouth.edu/~doyle/docs/three/three.pdf

senki 16y ago

The Wikipedia has a good article: http://en.wikipedia.org/wiki/Divisibility_rule http://en.wikipedia.org/wiki/Divisibility_rule