2 Strange mathematical facts .

[Dave7]

Just enjoyed the post in "General Cycling Discussions" when the OP asked for help with a maths formula.
http://www.cyclechat.net/threads/cant-work-this-out-myself.113184/ and it got me thinking
Now I'm not very good at maths (never was at school 50 years ago) but I do remember 2 peculiar/strange facts..........
1. You can multiply literally any number by 9 and when you add all the resultant digits up the answer is always...........9.... e.g. 8x9 = 72. 7+2 = 9............or 157 x 9 = 1,413. add 1+4+1+3 = 9

2. There is just 1 number (quite a large one) that can be divided by any single digit e.g. from 1 to 9). It's actually a Biblical number so if anyone knows their Bible (book of Daniel)?????
I will post the answer after people have had a chance to reply and perhaps add their own strange facts.

 

[ohnovino]

2. There is just 1 number (quite a large one) that can be divided by any single digit e.g. from 1 to 9).

Any multiple of 5040 would do.

 

[Peter Armstrong]

99x9 = 891 8+9+1 = 18? but then 8 +1 =9?

 

[Dave7]

Any multiple of 5040 would do.

Ah yes......I should qualify this. What is the smallest number that will work ?

 

[Dave7]

99x9 = 891 8+9+1 = 18? but then 8 +1 =9?

yes......so long as you continue to add the individual digits till there is only the single one (as you have done)

 

[LosingFocus]

2520

 

[ohnovino]

Ah yes......I should qualify this. What is the smallest number that will work ?

2520 (I was wrong when I said 5040, that's what I get for using a poundland calculator!)

Every whole number is the product of a unique set of prime numbers:
2 = 2
3 = 3
4 = 2x2
5 = 5
6 = 2x3
7 = 7
8 = 2x2x2
9 = 3x3

The lowest common multiple would be the smallest number that covers all those terms:
lcm(2,3,4,5,6,7,8,9) = 2x2x2x3x3x5x7 = 2520

 

[LosingFocus]

2520 (I was wrong when I said 5040, that's what I get for using a poundland calculator!)

Every whole number is the product of a unique set of prime numbers:
2 = 2
3 = 3
4 = 2x2
5 = 5
6 = 2x3
7 = 7
8 = 2x2x2
9 = 3x3

The lowest common multiple would be the smallest number that covers all those terms:
lcm(2,3,4,5,6,7,8,9) = 2x2x2x3x3x5x7 = 2520

This is how I got there.

 

[Beebo]

111,111,111 x 111,111,111 = 12345678987654321

 

[thom]

I refer the honourable gentleman to the reply given below :
http://www.cyclechat.net/threads/fn...hursday-29th-december-2011.90075/post-1662842
The Biblicle number you describe is 2520 = 8 x 9 x 5 x 7

 

[marinyork]

On the topic of what we were talking about earlier with Fields Medal winners and what they've later done
1. Every odd number greater than 1 is the sum of at most five primes
2. If God plays origami then Calabi-Yau manifolds may be the extra dimensions people talk about so much.

 

[Maz]

This is how I got there.

I always wonder what's written on a contestant's piece of paper on Countdown, when the contestant claims to have got the same answer using the same calculation as their opponent...then they show it to one of the panel...

I think the only thing written on the paper is "Snitch on me and You die!".

 

[classic33]

Whats the odd prime number.

 

[thom]

The Biblicle number you describe is 2520 = 8 x 9 x 5 x 7

Or any multiple thereof of course - 5040, 7560,... etc have the same property you mention. There are infinitely many such numbers but an unique smallest positive integer with that property, which is 2520.

 

[thom]

On the topic of what we were talking about earlier with Fields Medal winners and what they've later done
1. Every odd number greater than 1 is the sum of at most five primes

If bet you can't give me an example that can't be done in 3 though ;-)
(see Goldbach conjecture )